R. A. Horn and I. Olkin, "When does A 3 A = B 3 B and why does one want to know?," Amer. Math. Monthly, vol. 103, no. 6, pp. 470--482, 1996.  Home/Search   Document Not in Database   Summary   Related Articles

....there exists an unitary matrix and a real diagonal matrix so that (60) Substituting into the unitary condition on ,wehave . Since is a non negative definite matrix, the diagonal entries of the diagonal matrix are non negative. Therefore, we can express as diag . Let diag ; then, and . From [30], we know that there exists an matrix so that and . When is even, is a square unitary matrix. When is odd, there exists a vector so that is a unitary matrix. Let even odd ; then (61) where the zero vector does not appear above for even . Without loss of generality, we assume that diag , where ....

R. A. Horn and I. Olkin, "When does A 3 A = B 3 B and why does one want to know?," Amer. Math. Monthly, vol. 103, no. 6, pp. 470--482, 1996.

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