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On Pearl's Paper 'A Decomposition Theorem for Matrices'*
- Source :
- Canadian Mathematical Bulletin. 12:805-808
- Publication Year :
- 1969
- Publisher :
- Canadian Mathematical Society, 1969.
-
Abstract
- Let A be an m × n matrix of complex numbers. Let Aτ and A* denote the transpose and conjugate transpose, respectively, of A. We say A is diagonal if A contains only zeros in all positions (i, j) with i ≠ j. In a recently published paper [4], M.H. Pearl established the following fact: There exist real orthogonal matrices O1 and O2 (O1 m-square, O2 n-square) such that O1AO2 is diagonal, if and only if both AA* and A*A are real. It is the purpose of this paper to show that a theorem substantially stronger than this result of Pearl's is included in the real case of a theorem of N.A. Wiegmann [2]. (For other papers related to Wiegmann's, see [l; 3].)
Details
- ISSN :
- 14964287 and 00084395
- Volume :
- 12
- Database :
- OpenAIRE
- Journal :
- Canadian Mathematical Bulletin
- Accession number :
- edsair.doi...........3d7c862b1fc203ed3b7dd023a4700512