a.) Let n ≥ 1. Define U(n) = {U € Mnxn (C): U is unitary}. Show that U(n) is closed under (i) taking inverse, and (ii) taking products. U(n) is called the unitary group of rank n. b.) Define O(n) = {Q € Mnxn (R) : Q is orthogonal}. Show that O(n) is closed under (i) taking inverse, and (ii) taking products. O(n) is called the orthogonal group of rank n.

a.) Let n ≥ 1. Define U(n) = {U € Mnxn (C): U is unitary}. Show that U(n) is closed under (i) taking inverse, and (ii) taking products. U(n) is called the unitary group of rank n. b.) Define O(n) = {Q € Mnxn (R) : Q is orthogonal}. Show that O(n) is closed under (i) taking inverse, and (ii) taking products. O(n) is called the orthogonal group of rank n.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.4: The Singular Value Decomposition

Problem 27EQ

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