✦ LIBER ✦

-Orthogonal matrices

✍ Scribed by Ma. Nerissa M. Abara; Dennis I. Merino; Agnes T. Paras

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 231 KB
Volume: 432
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2009.12.029

No coin nor oath required. For personal study only.

✦ Synopsis

Let S ∈ M n (R) be such that S 2 = I or S 2 = -I.

is unitary, and both factors are φ S -orthogonal. We show that if A is φ Sorthogonal and normal, and if -1 is not an eigenvalue of A, then there exists a normal φ S -skew symmetric N (that is, φ S (N) = -N) such that A = e iN . We also take a look at the particular cases S = H k ≡ 0 I k -I k 0 and S = L k ≡ I k ⊕ -I n-k .

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