Label the following statements as being true or false. a) An inner product is a scalar-valued function on the set of ordered pairs of vectors. b) An inner product space must be over the field of real or complex numbers. c) An inner product is linear in both components. d) There is exactly one inner product on the vector space Rn. e) The triangle inequality only holds in finite-dimensional inner product spaces. f) Only square matrices have a conjugate-transpose. g) If <x,y>=0 for all x in an inner product space, then y=0.

Label the following statements as being true or false. a) An inner product is a scalar-valued function on the set of ordered pairs of vectors. b) An inner product space must be over the field of real or complex numbers. c) An inner product is linear in both components. d) There is exactly one inner product on the vector space Rn. e) The triangle inequality only holds in finite-dimensional inner product spaces. f) Only square matrices have a conjugate-transpose. g) If <x,y>=0 for all x in an inner product space, then y=0.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

Problem 15EQ

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