On the boundary of the C-numerical range of a matrix
Let C and A be n × n complex matrices. The C-numerical range of A is the setWc(A) = {tr(CUAU*) unitary}in[image omitted] . Given c = (c1…cn)ε Cn, the set Wc(A) is denoted by Wc(A) and said to be the c-numerical range in the case that C is the diagonal matrix with diagonal entries c = (c1,…,cn). In t...
Ausführliche Beschreibung
Autor*in: |
Nakazato, Hiroshi [verfasserIn] Nishikawa, Yasutaka [verfasserIn] Takaguchi, Makoto [verfasserIn] |
---|
Format: |
E-Artikel |
---|---|
Sprache: |
Englisch |
Erschienen: |
2011 |
---|
Übergeordnetes Werk: |
Enthalten in: Linear and multilinear algebra - London [u.a.] : Taylor & Francis, 1973, 39(1995), 3 vom: Aug., Seite 231-240 |
---|---|
Übergeordnetes Werk: |
number:3 ; volume:39 ; year:1995 ; month:08 ; pages:231-240 |
Links: |
---|
DOI / URN: |
10.1080/03081089508818395 |
---|
Katalog-ID: |
NLEJ252899539 |
---|
LEADER | 01000naa a22002652 4500 | ||
---|---|---|---|
001 | NLEJ252899539 | ||
003 | DE-627 | ||
005 | 20231206143610.0 | ||
007 | cr uuu---uuuuu | ||
008 | 231206s2011 xx |||||o 00| ||eng c | ||
024 | 7 | |a 10.1080/03081089508818395 |2 doi | |
035 | |a (DE-627)NLEJ252899539 | ||
035 | |a (TFO)778408962 | ||
040 | |a DE-627 |b ger |c DE-627 |e rda | ||
041 | |a eng | ||
100 | 1 | |a Nakazato, Hiroshi |e verfasserin |4 aut | |
245 | 1 | 0 | |a On the boundary of the C-numerical range of a matrix |
264 | 1 | |c 2011 | |
336 | |a Text |b txt |2 rdacontent | ||
337 | |a Computermedien |b c |2 rdamedia | ||
338 | |a Online-Ressource |b cr |2 rdacarrier | ||
520 | |a Let C and A be n × n complex matrices. The C-numerical range of A is the setWc(A) = {tr(CUAU*) unitary}in[image omitted] . Given c = (c1…cn)ε Cn, the set Wc(A) is denoted by Wc(A) and said to be the c-numerical range in the case that C is the diagonal matrix with diagonal entries c = (c1,…,cn). In this paper we study the boundary ∂Wc(A) of Wc(A). Above all, we show the following:A non-differentiable point of ∂Wc(A) is a pivot of a sector which is formed by ∂Wc(A), in the case of c =(c1 … cn)[image omitted] . All differentiable points of ∂Wc(A) are classified via their degrees of smoothness. For example, there exists a case in which a C1-smooth point of ∂W(1,0,…0)(A) is not analytically smooth. However, the number of non-analytically smooth points of ∂Wc(A) is at most finite. | ||
700 | 1 | |a Nishikawa, Yasutaka |e verfasserin |4 aut | |
700 | 1 | |a Takaguchi, Makoto |e verfasserin |4 aut | |
773 | 0 | 8 | |i Enthalten in |t Linear and multilinear algebra |d London [u.a.] : Taylor & Francis, 1973 |g 39(1995), 3 vom: Aug., Seite 231-240 |h Online-Ressource |w (DE-627)NLEJ252888618 |w (DE-600)2032579-4 |w (DE-576)095660305 |x 1563-5139 |7 nnns |
773 | 1 | 8 | |g number:3 |g volume:39 |g year:1995 |g month:08 |g pages:231-240 |
856 | 4 | 0 | |u https://www.tib.eu/de/suchen/id/tandf%3Ae901f4b673463a36304987d104a74d300894e8b2 |x Digitalisierung |z Deutschlandweit zugänglich |
912 | |a ZDB-1-TFO | ||
912 | |a GBV_NL_ARTICLE | ||
951 | |a AR | ||
952 | |e 3 |d 39 |j 1995 |c 8 |h 231-240 |
author_variant |
h n hn y n yn m t mt |
---|---|
matchkey_str |
article:15635139:2011----::nhbudrotenmrcla |
hierarchy_sort_str |
2011 |
publishDate |
2011 |
allfields |
10.1080/03081089508818395 doi (DE-627)NLEJ252899539 (TFO)778408962 DE-627 ger DE-627 rda eng Nakazato, Hiroshi verfasserin aut On the boundary of the C-numerical range of a matrix 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let C and A be n × n complex matrices. The C-numerical range of A is the setWc(A) = {tr(CUAU*) unitary}in[image omitted] . Given c = (c1…cn)ε Cn, the set Wc(A) is denoted by Wc(A) and said to be the c-numerical range in the case that C is the diagonal matrix with diagonal entries c = (c1,…,cn). In this paper we study the boundary ∂Wc(A) of Wc(A). Above all, we show the following:A non-differentiable point of ∂Wc(A) is a pivot of a sector which is formed by ∂Wc(A), in the case of c =(c1 … cn)[image omitted] . All differentiable points of ∂Wc(A) are classified via their degrees of smoothness. For example, there exists a case in which a C1-smooth point of ∂W(1,0,…0)(A) is not analytically smooth. However, the number of non-analytically smooth points of ∂Wc(A) is at most finite. Nishikawa, Yasutaka verfasserin aut Takaguchi, Makoto verfasserin aut Enthalten in Linear and multilinear algebra London [u.a.] : Taylor & Francis, 1973 39(1995), 3 vom: Aug., Seite 231-240 Online-Ressource (DE-627)NLEJ252888618 (DE-600)2032579-4 (DE-576)095660305 1563-5139 nnns number:3 volume:39 year:1995 month:08 pages:231-240 https://www.tib.eu/de/suchen/id/tandf%3Ae901f4b673463a36304987d104a74d300894e8b2 Digitalisierung Deutschlandweit zugänglich ZDB-1-TFO GBV_NL_ARTICLE AR 3 39 1995 8 231-240 |
spelling |
10.1080/03081089508818395 doi (DE-627)NLEJ252899539 (TFO)778408962 DE-627 ger DE-627 rda eng Nakazato, Hiroshi verfasserin aut On the boundary of the C-numerical range of a matrix 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let C and A be n × n complex matrices. The C-numerical range of A is the setWc(A) = {tr(CUAU*) unitary}in[image omitted] . Given c = (c1…cn)ε Cn, the set Wc(A) is denoted by Wc(A) and said to be the c-numerical range in the case that C is the diagonal matrix with diagonal entries c = (c1,…,cn). In this paper we study the boundary ∂Wc(A) of Wc(A). Above all, we show the following:A non-differentiable point of ∂Wc(A) is a pivot of a sector which is formed by ∂Wc(A), in the case of c =(c1 … cn)[image omitted] . All differentiable points of ∂Wc(A) are classified via their degrees of smoothness. For example, there exists a case in which a C1-smooth point of ∂W(1,0,…0)(A) is not analytically smooth. However, the number of non-analytically smooth points of ∂Wc(A) is at most finite. Nishikawa, Yasutaka verfasserin aut Takaguchi, Makoto verfasserin aut Enthalten in Linear and multilinear algebra London [u.a.] : Taylor & Francis, 1973 39(1995), 3 vom: Aug., Seite 231-240 Online-Ressource (DE-627)NLEJ252888618 (DE-600)2032579-4 (DE-576)095660305 1563-5139 nnns number:3 volume:39 year:1995 month:08 pages:231-240 https://www.tib.eu/de/suchen/id/tandf%3Ae901f4b673463a36304987d104a74d300894e8b2 Digitalisierung Deutschlandweit zugänglich ZDB-1-TFO GBV_NL_ARTICLE AR 3 39 1995 8 231-240 |
allfields_unstemmed |
10.1080/03081089508818395 doi (DE-627)NLEJ252899539 (TFO)778408962 DE-627 ger DE-627 rda eng Nakazato, Hiroshi verfasserin aut On the boundary of the C-numerical range of a matrix 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let C and A be n × n complex matrices. The C-numerical range of A is the setWc(A) = {tr(CUAU*) unitary}in[image omitted] . Given c = (c1…cn)ε Cn, the set Wc(A) is denoted by Wc(A) and said to be the c-numerical range in the case that C is the diagonal matrix with diagonal entries c = (c1,…,cn). In this paper we study the boundary ∂Wc(A) of Wc(A). Above all, we show the following:A non-differentiable point of ∂Wc(A) is a pivot of a sector which is formed by ∂Wc(A), in the case of c =(c1 … cn)[image omitted] . All differentiable points of ∂Wc(A) are classified via their degrees of smoothness. For example, there exists a case in which a C1-smooth point of ∂W(1,0,…0)(A) is not analytically smooth. However, the number of non-analytically smooth points of ∂Wc(A) is at most finite. Nishikawa, Yasutaka verfasserin aut Takaguchi, Makoto verfasserin aut Enthalten in Linear and multilinear algebra London [u.a.] : Taylor & Francis, 1973 39(1995), 3 vom: Aug., Seite 231-240 Online-Ressource (DE-627)NLEJ252888618 (DE-600)2032579-4 (DE-576)095660305 1563-5139 nnns number:3 volume:39 year:1995 month:08 pages:231-240 https://www.tib.eu/de/suchen/id/tandf%3Ae901f4b673463a36304987d104a74d300894e8b2 Digitalisierung Deutschlandweit zugänglich ZDB-1-TFO GBV_NL_ARTICLE AR 3 39 1995 8 231-240 |
allfieldsGer |
10.1080/03081089508818395 doi (DE-627)NLEJ252899539 (TFO)778408962 DE-627 ger DE-627 rda eng Nakazato, Hiroshi verfasserin aut On the boundary of the C-numerical range of a matrix 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let C and A be n × n complex matrices. The C-numerical range of A is the setWc(A) = {tr(CUAU*) unitary}in[image omitted] . Given c = (c1…cn)ε Cn, the set Wc(A) is denoted by Wc(A) and said to be the c-numerical range in the case that C is the diagonal matrix with diagonal entries c = (c1,…,cn). In this paper we study the boundary ∂Wc(A) of Wc(A). Above all, we show the following:A non-differentiable point of ∂Wc(A) is a pivot of a sector which is formed by ∂Wc(A), in the case of c =(c1 … cn)[image omitted] . All differentiable points of ∂Wc(A) are classified via their degrees of smoothness. For example, there exists a case in which a C1-smooth point of ∂W(1,0,…0)(A) is not analytically smooth. However, the number of non-analytically smooth points of ∂Wc(A) is at most finite. Nishikawa, Yasutaka verfasserin aut Takaguchi, Makoto verfasserin aut Enthalten in Linear and multilinear algebra London [u.a.] : Taylor & Francis, 1973 39(1995), 3 vom: Aug., Seite 231-240 Online-Ressource (DE-627)NLEJ252888618 (DE-600)2032579-4 (DE-576)095660305 1563-5139 nnns number:3 volume:39 year:1995 month:08 pages:231-240 https://www.tib.eu/de/suchen/id/tandf%3Ae901f4b673463a36304987d104a74d300894e8b2 Digitalisierung Deutschlandweit zugänglich ZDB-1-TFO GBV_NL_ARTICLE AR 3 39 1995 8 231-240 |
allfieldsSound |
10.1080/03081089508818395 doi (DE-627)NLEJ252899539 (TFO)778408962 DE-627 ger DE-627 rda eng Nakazato, Hiroshi verfasserin aut On the boundary of the C-numerical range of a matrix 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let C and A be n × n complex matrices. The C-numerical range of A is the setWc(A) = {tr(CUAU*) unitary}in[image omitted] . Given c = (c1…cn)ε Cn, the set Wc(A) is denoted by Wc(A) and said to be the c-numerical range in the case that C is the diagonal matrix with diagonal entries c = (c1,…,cn). In this paper we study the boundary ∂Wc(A) of Wc(A). Above all, we show the following:A non-differentiable point of ∂Wc(A) is a pivot of a sector which is formed by ∂Wc(A), in the case of c =(c1 … cn)[image omitted] . All differentiable points of ∂Wc(A) are classified via their degrees of smoothness. For example, there exists a case in which a C1-smooth point of ∂W(1,0,…0)(A) is not analytically smooth. However, the number of non-analytically smooth points of ∂Wc(A) is at most finite. Nishikawa, Yasutaka verfasserin aut Takaguchi, Makoto verfasserin aut Enthalten in Linear and multilinear algebra London [u.a.] : Taylor & Francis, 1973 39(1995), 3 vom: Aug., Seite 231-240 Online-Ressource (DE-627)NLEJ252888618 (DE-600)2032579-4 (DE-576)095660305 1563-5139 nnns number:3 volume:39 year:1995 month:08 pages:231-240 https://www.tib.eu/de/suchen/id/tandf%3Ae901f4b673463a36304987d104a74d300894e8b2 Digitalisierung Deutschlandweit zugänglich ZDB-1-TFO GBV_NL_ARTICLE AR 3 39 1995 8 231-240 |
language |
English |
source |
Enthalten in Linear and multilinear algebra 39(1995), 3 vom: Aug., Seite 231-240 number:3 volume:39 year:1995 month:08 pages:231-240 |
sourceStr |
Enthalten in Linear and multilinear algebra 39(1995), 3 vom: Aug., Seite 231-240 number:3 volume:39 year:1995 month:08 pages:231-240 |
format_phy_str_mv |
Article |
institution |
findex.gbv.de |
isfreeaccess_bool |
false |
container_title |
Linear and multilinear algebra |
authorswithroles_txt_mv |
Nakazato, Hiroshi @@aut@@ Nishikawa, Yasutaka @@aut@@ Takaguchi, Makoto @@aut@@ |
publishDateDaySort_date |
1995-08-01T00:00:00Z |
hierarchy_top_id |
NLEJ252888618 |
id |
NLEJ252899539 |
language_de |
englisch |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">NLEJ252899539</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20231206143610.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">231206s2011 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1080/03081089508818395</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ252899539</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(TFO)778408962</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Nakazato, Hiroshi</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On the boundary of the C-numerical range of a matrix</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2011</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Let C and A be n × n complex matrices. The C-numerical range of A is the setWc(A) = {tr(CUAU*) unitary}in[image omitted] . Given c = (c1…cn)ε Cn, the set Wc(A) is denoted by Wc(A) and said to be the c-numerical range in the case that C is the diagonal matrix with diagonal entries c = (c1,…,cn). In this paper we study the boundary ∂Wc(A) of Wc(A). Above all, we show the following:A non-differentiable point of ∂Wc(A) is a pivot of a sector which is formed by ∂Wc(A), in the case of c =(c1 … cn)[image omitted] . All differentiable points of ∂Wc(A) are classified via their degrees of smoothness. For example, there exists a case in which a C1-smooth point of ∂W(1,0,…0)(A) is not analytically smooth. However, the number of non-analytically smooth points of ∂Wc(A) is at most finite.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Nishikawa, Yasutaka</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Takaguchi, Makoto</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Linear and multilinear algebra</subfield><subfield code="d">London [u.a.] : Taylor & Francis, 1973</subfield><subfield code="g">39(1995), 3 vom: Aug., Seite 231-240</subfield><subfield code="h">Online-Ressource</subfield><subfield code="w">(DE-627)NLEJ252888618</subfield><subfield code="w">(DE-600)2032579-4</subfield><subfield code="w">(DE-576)095660305</subfield><subfield code="x">1563-5139</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">number:3</subfield><subfield code="g">volume:39</subfield><subfield code="g">year:1995</subfield><subfield code="g">month:08</subfield><subfield code="g">pages:231-240</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.tib.eu/de/suchen/id/tandf%3Ae901f4b673463a36304987d104a74d300894e8b2</subfield><subfield code="x">Digitalisierung</subfield><subfield code="z">Deutschlandweit zugänglich</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-TFO</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="e">3</subfield><subfield code="d">39</subfield><subfield code="j">1995</subfield><subfield code="c">8</subfield><subfield code="h">231-240</subfield></datafield></record></collection>
|
author |
Nakazato, Hiroshi |
spellingShingle |
Nakazato, Hiroshi On the boundary of the C-numerical range of a matrix |
authorStr |
Nakazato, Hiroshi |
ppnlink_with_tag_str_mv |
@@773@@(DE-627)NLEJ252888618 |
format |
electronic Article |
delete_txt_mv |
keep |
author_role |
aut aut aut |
collection |
NL |
remote_str |
true |
illustrated |
Not Illustrated |
issn |
1563-5139 |
topic_title |
On the boundary of the C-numerical range of a matrix |
format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
format_main_str_mv |
Text Zeitschrift/Artikel |
carriertype_str_mv |
cr |
hierarchy_parent_title |
Linear and multilinear algebra |
hierarchy_parent_id |
NLEJ252888618 |
hierarchy_top_title |
Linear and multilinear algebra |
isfreeaccess_txt |
false |
familylinks_str_mv |
(DE-627)NLEJ252888618 (DE-600)2032579-4 (DE-576)095660305 |
title |
On the boundary of the C-numerical range of a matrix |
ctrlnum |
(DE-627)NLEJ252899539 (TFO)778408962 |
title_full |
On the boundary of the C-numerical range of a matrix |
author_sort |
Nakazato, Hiroshi |
journal |
Linear and multilinear algebra |
journalStr |
Linear and multilinear algebra |
lang_code |
eng |
isOA_bool |
false |
recordtype |
marc |
publishDateSort |
2011 |
contenttype_str_mv |
txt |
container_start_page |
231 |
author_browse |
Nakazato, Hiroshi Nishikawa, Yasutaka Takaguchi, Makoto |
container_volume |
39 |
format_se |
Elektronische Aufsätze |
author-letter |
Nakazato, Hiroshi |
doi_str_mv |
10.1080/03081089508818395 |
author2-role |
verfasserin |
title_sort |
on the boundary of the c-numerical range of a matrix |
title_auth |
On the boundary of the C-numerical range of a matrix |
abstract |
Let C and A be n × n complex matrices. The C-numerical range of A is the setWc(A) = {tr(CUAU*) unitary}in[image omitted] . Given c = (c1…cn)ε Cn, the set Wc(A) is denoted by Wc(A) and said to be the c-numerical range in the case that C is the diagonal matrix with diagonal entries c = (c1,…,cn). In this paper we study the boundary ∂Wc(A) of Wc(A). Above all, we show the following:A non-differentiable point of ∂Wc(A) is a pivot of a sector which is formed by ∂Wc(A), in the case of c =(c1 … cn)[image omitted] . All differentiable points of ∂Wc(A) are classified via their degrees of smoothness. For example, there exists a case in which a C1-smooth point of ∂W(1,0,…0)(A) is not analytically smooth. However, the number of non-analytically smooth points of ∂Wc(A) is at most finite. |
abstractGer |
Let C and A be n × n complex matrices. The C-numerical range of A is the setWc(A) = {tr(CUAU*) unitary}in[image omitted] . Given c = (c1…cn)ε Cn, the set Wc(A) is denoted by Wc(A) and said to be the c-numerical range in the case that C is the diagonal matrix with diagonal entries c = (c1,…,cn). In this paper we study the boundary ∂Wc(A) of Wc(A). Above all, we show the following:A non-differentiable point of ∂Wc(A) is a pivot of a sector which is formed by ∂Wc(A), in the case of c =(c1 … cn)[image omitted] . All differentiable points of ∂Wc(A) are classified via their degrees of smoothness. For example, there exists a case in which a C1-smooth point of ∂W(1,0,…0)(A) is not analytically smooth. However, the number of non-analytically smooth points of ∂Wc(A) is at most finite. |
abstract_unstemmed |
Let C and A be n × n complex matrices. The C-numerical range of A is the setWc(A) = {tr(CUAU*) unitary}in[image omitted] . Given c = (c1…cn)ε Cn, the set Wc(A) is denoted by Wc(A) and said to be the c-numerical range in the case that C is the diagonal matrix with diagonal entries c = (c1,…,cn). In this paper we study the boundary ∂Wc(A) of Wc(A). Above all, we show the following:A non-differentiable point of ∂Wc(A) is a pivot of a sector which is formed by ∂Wc(A), in the case of c =(c1 … cn)[image omitted] . All differentiable points of ∂Wc(A) are classified via their degrees of smoothness. For example, there exists a case in which a C1-smooth point of ∂W(1,0,…0)(A) is not analytically smooth. However, the number of non-analytically smooth points of ∂Wc(A) is at most finite. |
collection_details |
ZDB-1-TFO GBV_NL_ARTICLE |
container_issue |
3 |
title_short |
On the boundary of the C-numerical range of a matrix |
url |
https://www.tib.eu/de/suchen/id/tandf%3Ae901f4b673463a36304987d104a74d300894e8b2 |
remote_bool |
true |
author2 |
Nishikawa, Yasutaka Takaguchi, Makoto |
author2Str |
Nishikawa, Yasutaka Takaguchi, Makoto |
ppnlink |
NLEJ252888618 |
mediatype_str_mv |
c |
isOA_txt |
false |
hochschulschrift_bool |
false |
doi_str |
10.1080/03081089508818395 |
up_date |
2024-07-05T22:14:44.225Z |
_version_ |
1803778978454962176 |
fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">NLEJ252899539</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20231206143610.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">231206s2011 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1080/03081089508818395</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ252899539</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(TFO)778408962</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Nakazato, Hiroshi</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On the boundary of the C-numerical range of a matrix</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2011</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Let C and A be n × n complex matrices. The C-numerical range of A is the setWc(A) = {tr(CUAU*) unitary}in[image omitted] . Given c = (c1…cn)ε Cn, the set Wc(A) is denoted by Wc(A) and said to be the c-numerical range in the case that C is the diagonal matrix with diagonal entries c = (c1,…,cn). In this paper we study the boundary ∂Wc(A) of Wc(A). Above all, we show the following:A non-differentiable point of ∂Wc(A) is a pivot of a sector which is formed by ∂Wc(A), in the case of c =(c1 … cn)[image omitted] . All differentiable points of ∂Wc(A) are classified via their degrees of smoothness. For example, there exists a case in which a C1-smooth point of ∂W(1,0,…0)(A) is not analytically smooth. However, the number of non-analytically smooth points of ∂Wc(A) is at most finite.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Nishikawa, Yasutaka</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Takaguchi, Makoto</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Linear and multilinear algebra</subfield><subfield code="d">London [u.a.] : Taylor & Francis, 1973</subfield><subfield code="g">39(1995), 3 vom: Aug., Seite 231-240</subfield><subfield code="h">Online-Ressource</subfield><subfield code="w">(DE-627)NLEJ252888618</subfield><subfield code="w">(DE-600)2032579-4</subfield><subfield code="w">(DE-576)095660305</subfield><subfield code="x">1563-5139</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">number:3</subfield><subfield code="g">volume:39</subfield><subfield code="g">year:1995</subfield><subfield code="g">month:08</subfield><subfield code="g">pages:231-240</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.tib.eu/de/suchen/id/tandf%3Ae901f4b673463a36304987d104a74d300894e8b2</subfield><subfield code="x">Digitalisierung</subfield><subfield code="z">Deutschlandweit zugänglich</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-TFO</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="e">3</subfield><subfield code="d">39</subfield><subfield code="j">1995</subfield><subfield code="c">8</subfield><subfield code="h">231-240</subfield></datafield></record></collection>
|
score |
7.3999805 |