Let V be finite-dimensional and let TE L(V). Prove that T is normal ifand only if with respect to any orthonormal basis B of V, the matrix of T, A = [T]B,satisfiesAA* = A*A.

Introduction: In linear algebra, an orthonormal basis is a set of vectors in a vector space that are…

Answered: Let V be finite-dimensional and let T €…

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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Let V be finite-dimensional and let T € L(V). Prove that T is normal if and only if with respect to any orthonormal basis B of V, the matrix of T, A = [T]B, satisfies AA* = A*A.