A Decomposition Theorem for Matrices
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 344-349
Voir la notice de l'article provenant de la source Cambridge University Press
According to a classical theorem originally proved by L. Autonne (1; 3) in 1915, every m × n matrix of rank r with entries from the complex field can be decomposed as where U1 and U2 are unitary matrices of order m and n respectively and D is an m × n matrix having the form 1 where Δ is a non-singular diagonal matrix whose rank is r. If r = m, then the row of zero matrices of (1) does not actually appear. If r = n, then the column of zero matrices of (1) does not appear. The main purpose of this paper is to give a necessary and sufficient condition under which both U1 and U2 may be chosen to be real orthogonal matrices.
Pearl, Martin H. A Decomposition Theorem for Matrices. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 344-349. doi: 10.4153/CJM-1967-025-2
@article{10_4153_CJM_1967_025_2,
author = {Pearl, Martin H.},
title = {A {Decomposition} {Theorem} for {Matrices}},
journal = {Canadian journal of mathematics},
pages = {344--349},
year = {1967},
volume = {19},
number = {1},
doi = {10.4153/CJM-1967-025-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-025-2/}
}
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