The bideterminants of matrices over semirings
Abstract This paper deals with the relationships between the concepts of linear dependence and independence of vectors, and the bideterminant of a matrix including the links between the bideterminant and rank of a square matrix in semilinear spaces of $$n$$-dimensional vectors over commutative zeros...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Wang, Xue-ping [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Soft computing - Springer Berlin Heidelberg, 1997, 18(2013), 4 vom: 01. Nov., Seite 729-742 |
|---|---|
| Übergeordnetes Werk: |
volume:18 ; year:2013 ; number:4 ; day:01 ; month:11 ; pages:729-742 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00500-013-1163-y |
|---|
| Katalog-ID: |
OLC2034875230 |
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10.1007/s00500-013-1163-y doi (DE-627)OLC2034875230 (DE-He213)s00500-013-1163-y-p DE-627 ger DE-627 rakwb eng 004 VZ 004 VZ 11 ssgn Wang, Xue-ping verfasserin aut The bideterminants of matrices over semirings 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract This paper deals with the relationships between the concepts of linear dependence and independence of vectors, and the bideterminant of a matrix including the links between the bideterminant and rank of a square matrix in semilinear spaces of $$n$$-dimensional vectors over commutative zerosumfree semirings. First, it discusses some properties of bideterminant of a matrix, then introduces the concepts of semi-linear dependence and strong linear independence of a set of vectors, respectively, and gives a necessary and sufficient condition that the bideterminant of a matrix is equal to $$0$$. In the end, it shows a necessary and sufficient condition that the rank of an $$n$$-square matrix is equal to $$n$$. Semiring Bideterminant Semi-linear dependence Strong linear independence Rank Shu, Qian-yu aut Enthalten in Soft computing Springer Berlin Heidelberg, 1997 18(2013), 4 vom: 01. Nov., Seite 729-742 (DE-627)231970536 (DE-600)1387526-7 (DE-576)060238259 1432-7643 nnns volume:18 year:2013 number:4 day:01 month:11 pages:729-742 https://doi.org/10.1007/s00500-013-1163-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_4277 AR 18 2013 4 01 11 729-742 |
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Abstract This paper deals with the relationships between the concepts of linear dependence and independence of vectors, and the bideterminant of a matrix including the links between the bideterminant and rank of a square matrix in semilinear spaces of $$n$$-dimensional vectors over commutative zerosumfree semirings. First, it discusses some properties of bideterminant of a matrix, then introduces the concepts of semi-linear dependence and strong linear independence of a set of vectors, respectively, and gives a necessary and sufficient condition that the bideterminant of a matrix is equal to $$0$$. In the end, it shows a necessary and sufficient condition that the rank of an $$n$$-square matrix is equal to $$n$$. © Springer-Verlag Berlin Heidelberg 2013 |
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Abstract This paper deals with the relationships between the concepts of linear dependence and independence of vectors, and the bideterminant of a matrix including the links between the bideterminant and rank of a square matrix in semilinear spaces of $$n$$-dimensional vectors over commutative zerosumfree semirings. First, it discusses some properties of bideterminant of a matrix, then introduces the concepts of semi-linear dependence and strong linear independence of a set of vectors, respectively, and gives a necessary and sufficient condition that the bideterminant of a matrix is equal to $$0$$. In the end, it shows a necessary and sufficient condition that the rank of an $$n$$-square matrix is equal to $$n$$. © Springer-Verlag Berlin Heidelberg 2013 |
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Abstract This paper deals with the relationships between the concepts of linear dependence and independence of vectors, and the bideterminant of a matrix including the links between the bideterminant and rank of a square matrix in semilinear spaces of $$n$$-dimensional vectors over commutative zerosumfree semirings. First, it discusses some properties of bideterminant of a matrix, then introduces the concepts of semi-linear dependence and strong linear independence of a set of vectors, respectively, and gives a necessary and sufficient condition that the bideterminant of a matrix is equal to $$0$$. In the end, it shows a necessary and sufficient condition that the rank of an $$n$$-square matrix is equal to $$n$$. © Springer-Verlag Berlin Heidelberg 2013 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2034875230</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230502111645.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2013 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00500-013-1163-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2034875230</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00500-013-1163-y-p</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">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">004</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">004</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">11</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Wang, Xue-ping</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The bideterminants of matrices over semirings</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</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">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag Berlin Heidelberg 2013</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This paper deals with the relationships between the concepts of linear dependence and independence of vectors, and the bideterminant of a matrix including the links between the bideterminant and rank of a square matrix in semilinear spaces of $$n$$-dimensional vectors over commutative zerosumfree semirings. First, it discusses some properties of bideterminant of a matrix, then introduces the concepts of semi-linear dependence and strong linear independence of a set of vectors, respectively, and gives a necessary and sufficient condition that the bideterminant of a matrix is equal to $$0$$. 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