An operator T: IR" → IR" is called a self-adjoint operator if [T]®p is a symmetric matrix, where B is an orthonormal basis of IR". Decide whether the below operator is self- adjoint. Justify! T: IR³ → IR³3 (x, y, z) → (x+D·y +U · z, -D . x + M · y + 4z, U · x + 4y + 32) Where: D= 0; U= 8; M=5.

An operator T: IR" → IR" is called a self-adjoint operator if [T]®p is a symmetric matrix, where B is an orthonormal basis of IR". Decide whether the below operator is self- adjoint. Justify! T: IR³ → IR³3 (x, y, z) → (x+D·y +U · z, -D . x + M · y + 4z, U · x + 4y + 32) Where: D= 0; U= 8; M=5.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.5: Applications

Problem 30EQ

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