7. Assume that Vi, i = 1, 2 are vector spaces over F E {R, C) and (, ),, i = 1, 2is an inner product on V₂. Set V = V₁ V₂ and define (, ): V x V → F by((u₁, U₂), (v₁, v₂)) = (u₁, v₁)₁ + (u2; v2) 21for u₁, v₁ € V₁, U2, v2 € V₂. Determine whether (, ) is an inner product onV. Prove your conclusion.8. Let (V, (, )) be an inner product space and L = (v₁, V2,..., Vn.) a sequence

Let X is a vector space. A map V×V→F is said to be an inner product space if the following property…

7. Assume that Vi, i = 1,2 are vector spaces over F E {R, C} and (,), i = 1, 2 is an inner product on V₂. Set V = V₁ V₂ and define (, ): V x V → F by ((U₁, U2), (v₁, v₂)) = (U₁, v₁)₁ + (u2; v₂) 2 for u₁, v₁ € V₁, U2, v2 € V₂. Determine whether (, ) is an inner product on V. Prove your conclusion.

7. Assume that Vi, i = 1,2 are vector spaces over F E {R, C} and (,), i = 1, 2 is an inner product on V₂. Set V = V₁ V₂ and define (, ): V x V → F by ((U₁, U2), (v₁, v₂)) = (U₁, v₁)₁ + (u2; v₂) 2 for u₁, v₁ € V₁, U2, v2 € V₂. Determine whether (, ) is an inner product on V. Prove your conclusion.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 24EQ

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