Let β be a basis for a subspace W of an inner product space V, and let z ∈V. Prove that z∈W⊥if and only if <z, v>= 0 for every v∈β.
Let β be a basis for a subspace W of an inner product space V, and let z ∈V. Prove that z∈W⊥if and only if <z, v>= 0 for every v∈β.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 24CM
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Let β be a basis for a subspace W of an inner product space V, and let z ∈V. Prove that z∈W⊥if and only if <z, v>= 0 for every v∈β.
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