Answered: Let T be a normal operator on a…

Let T be a normal operator on a finite-dimensional complex inner product space V. Use the spectral decomposition to prove the following: T* = -T if and only if all eigenvalues of T are imaginary.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.1: Introduction To Eigenvalues And Eigenvectors

Problem 38EQ

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Question

Linear algebra

Let T be a normal operator on a finite-dimensional complex inner product space V. Use the
spectral decomposition to prove the following:
T* = −T if and only if all eigenvalues of T are imaginary.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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