Geodesic
On Pearl's Paper "A Decomposition Theorem for Matrices"*
Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 805-808

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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].) 
Thompson, R. C. On Pearl's Paper "A Decomposition Theorem for Matrices"*. Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 805-808. doi: 10.4153/CMB-1969-104-5
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     title = {On {Pearl's} {Paper} {"A} {Decomposition} {Theorem} for {Matrices"*}},
     journal = {Canadian mathematical bulletin},
     pages = {805--808},
     year = {1969},
     volume = {12},
     number = {6},
     doi = {10.4153/CMB-1969-104-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-104-5/}
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