Involutions and angles between subspaces

초록

If S is an involution matrix, which means S-2 = I, then S is unitarily equivalent to (epsilon I-k)circle plus{circle plus(m)(i=1)(0(xi) x(i0)(-1))} where epsilon = +1, I-k is the identity of size k = |TrS|, and 0 < x(i)< 1, i = 1,.. ., m = n-k. This can be used to introduce principal angles between subspaces and yields formulas for the angles between the eigenspaces of S such as sin alpha(i) = 2/(xi+ x(-1) (i) ). (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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