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...
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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:	Link aufrufen

DOI / URN:	10.1080/03081089508818395

Katalog-ID:	NLEJ252899539

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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.
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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
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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.
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up_date	2024-07-05T22:14:44.225Z
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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>
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On the boundary of the C-numerical range of a matrix

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