Show that the following are equivalent for a symmetric matrix A. (a) A is orthogonal. (b) A2
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(a) A is orthogonal.
(b) A2 = I.
(c) All eigenvalues of A are ±1. [For (b) if and only if (c), use Theorem 2.]
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c a By Theorem 1 let P 1 AP D diag 1 n where the i ...View the full answer
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