Canonical Forms for Certain Matrices Under Unitary Congruence
- 1 January 1960
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 12, 438-446
- https://doi.org/10.4153/cjm-1960-038-2
Abstract
If A is a matrix with complex elements and if A = AT (where AT denotes the transpose of A), there exists a non-singular matrix P such that PAPT = D is a diagonal matrix (see (3), for example). It is also true (see the principal result of (5)) that for such an A there exists a unitary matrix U such that UAUT = D is a real diagonal matrix with nonnegative elements which is a canonical form for A relative to the given U, UT transformation.Keywords
This publication has 6 references indexed in Scilit:
- On Unitary and Symmetric Matrices With Real Quaternion ElementsCanadian Journal of Mathematics, 1956
- Some Theorems On Matrices With Real Quaternion ElementsCanadian Journal of Mathematics, 1955
- Ein Satz Ueber Quadratische Formen Mit Komplexen KoeffizientenAmerican Journal of Mathematics, 1945
- A principal axis transformation for non-hermitian matricesBulletin of the American Mathematical Society, 1939
- A polar representation of singular matricesBulletin of the American Mathematical Society, 1935
- On a Polar Representation of Non-Singular Square MatricesProceedings of the National Academy of Sciences, 1931