QUESTION 6 Let V = WW+ where V is a finite-dimensional inner product space over C and W is a non-trivial subspace of V. Define the linear operator T: V→ V by T(w+w) = iw - w where we W and w+ € W¹. (6.1) Find T*. (6.2) Show that T is unitary. (6.3) Find the eigenvalues and associated eigenspaces of T.

QUESTION 6 Let V = WW+ where V is a finite-dimensional inner product space over C and W is a non-trivial subspace of V. Define the linear operator T: V→ V by T(w+w) = iw - w where we W and w+ € W¹. (6.1) Find T*. (6.2) Show that T is unitary. (6.3) Find the eigenvalues and associated eigenspaces of T.

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 26EQ

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