Characterizations of EP, normal, and Hermitian matrices
Various characterizations of EP, normal, and Hermitian matrices are obtained by exploiting an elegant representation of matrices derived by Hartwig and Spindelböck [ 7 , Corollary 6]. One aim of the present article is to demonstrate its usefulness when investigating different matrix identities. The...
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| Published in | Linear & multilinear algebra Vol. 56; no. 3; pp. 299 - 304 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis Group
01.05.2008
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0308-1087 1563-5139 |
| DOI | 10.1080/03081080600872616 |
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| Abstract | Various characterizations of EP, normal, and Hermitian matrices are obtained by exploiting an elegant representation of matrices derived by Hartwig and Spindelböck [
7
, Corollary 6]. One aim of the present article is to demonstrate its usefulness when investigating different matrix identities. The second aim is to extend and generalize lists of characterizations of Equal Projectors (EP), normal, and Hermitian matrices known in the literature, by providing numerous sets of equivalent conditions referring to the notions of conjugate transpose, Moore-Penrose inverse, and group inverse. |
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| AbstractList | Various characterizations of EP, normal, and Hermitian matrices are obtained by exploiting an elegant representation of matrices derived by Hartwig and Spindelböck [
7
, Corollary 6]. One aim of the present article is to demonstrate its usefulness when investigating different matrix identities. The second aim is to extend and generalize lists of characterizations of Equal Projectors (EP), normal, and Hermitian matrices known in the literature, by providing numerous sets of equivalent conditions referring to the notions of conjugate transpose, Moore-Penrose inverse, and group inverse. |
| Author | Maria Baksalary, Oskar Trenkler, Götz |
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| Cites_doi | 10.1016/0024-3795(69)90009-3 10.1080/03081088308817561 10.1307/mmj/1028998132 10.1016/S0024-3795(03)00650-5 10.1007/978-1-4757-5797-2 10.4153/CMB-1975-061-4 10.1016/0024-3795(70)90020-0 10.1080/03081088308817529 10.1016/S0024-3795(98)10161-1 10.1016/0024-3795(87)90168-6 10.6028/jres.070B.004 10.1017/S0305004100040329 |
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| SubjectTerms | AMS Subject Classifications: 15A09 Commutativity Conjugate transpose Group inverse Moore-Penrose inverse Singular value decomposition Skew Hermitian matrix |
| Title | Characterizations of EP, normal, and Hermitian matrices |
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