Problem 3.14 Show that similarity preserves matrix multiplication (that is if A B C, then A/B/C). Similarity does not, in general, preserve symmetry, reality, or Hermiticity; show, however, that if S is unitary, and His Hermitian, then His Hermitian. Show that S carries an orthonormal basis into another orthonormal basis if and only if it is unitary.

Problem 3.14 Show that similarity preserves matrix multiplication (that is if A B C, then A/B/C). Similarity does not, in general, preserve symmetry, reality, or Hermiticity; show, however, that if S is unitary, and His Hermitian, then His Hermitian. Show that S carries an orthonormal basis into another orthonormal basis if and only if it is unitary.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 63EQ

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