Given a Hermitian space E, for any linear map f: E→ E, if f is skew- self-adjoint, then f has eigenvalues that are pure imaginary or zero, and if f is unitary, then f has eigenvalues of absolute value 1.
Given a Hermitian space E, for any linear map f: E→ E, if f is skew- self-adjoint, then f has eigenvalues that are pure imaginary or zero, and if f is unitary, then f has eigenvalues of absolute value 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Given a Hermitian space E, for any linear map f: E→ E, if f is skew-
self-adjoint, then f has eigenvalues that are pure imaginary or zero, and if f is unitary, then
f has eigenvalues of absolute value 1.
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