4. LADW #5.1.5: Explain (ie either give a counterexample or show that a paricular property in the definition fails) why each of the following is not an inner product on the given vector space: (a) (x, y) = x₁y1 – x2y2 on R². (b) (A, B) = trace(A + B) on M2x2. (c) (p, q) = f p'(t)q(t) dt on Pn, where f' denotes derivative.

4. LADW #5.1.5: Explain (ie either give a counterexample or show that a paricular property in the definition fails) why each of the following is not an inner product on the given vector space: (a) (x, y) = x₁y1 – x2y2 on R². (b) (A, B) = trace(A + B) on M2x2. (c) (p, q) = f p'(t)q(t) dt on Pn, where f' denotes derivative.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 1AEXP

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