Symmetric, Hermitian, and Unitary Operators

Rami Shakarchi

Chapter Chapter VII in Solutions Manual for Lang’s Linear Algebra, 1996, pp 101-116 from Springer

Abstract: Abstract (a) A matrix A is called skew-symmetric if t A= -A. Show that any matrix M can he expressed as a sum of a symmetric matrix and a skew-symmetric matrix one and that the latter expression is uniquely determined. [Hint:Let A = 1/2(M+1 M).] (b) Prove that if A is skew-symmetric,then A 2 is symmetric. (c) Let A be skew-symmetric. Show that Det(A) is 0 if A is an n x n matrix and n is odd.

Date: 1996
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DOI: 10.1007/978-1-4612-0755-9_7

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