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Let V be a vector space of dimension n and a scalar product. Recall that for U≤ V a subspace, U¹ ≤ V denotes its orthogonal complement (also a subspace). Show that dim(U) + dim(U¹) = n Note: choose a base for U and use this to describe U

Let V be a vector space of dimension n and a scalar product. Recall that for U≤ V a subspace, U¹ ≤ V denotes its orthogonal complement (also a subspace). Show that dim(U) + dim(U¹) = n Note: choose a base for U and use this to describe U

Elementary Linear Algebra (MindTap Course List)
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 V be a vector space of dimension n and a scalar product. Recall that for U≤ V a subspace, U¹ ≤ V denotes its orthogonal complement (also a subspace). Show that dim(U) + dim(U¹) = n Note : choose a base for U and use this to describe U¹
Transcribed Image Text:Let V be a vector space of dimension n and a scalar product. Recall that for U≤ V a subspace, U¹ ≤ V denotes its orthogonal complement (also a subspace). Show that dim(U) + dim(U¹) = n Note : choose a base for U and use this to describe U¹
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