Let V, W be finite-dimensional inner product spaces and T € L(V, W). Prove: (a) If T is injective, then T"T is invertible and T† = (T*T)-'T". (b) If T is surjective, then TT* is invertible and T† =T"(TT*)-!.
Let V, W be finite-dimensional inner product spaces and T € L(V, W). Prove: (a) If T is injective, then T"T is invertible and T† = (T*T)-'T". (b) If T is surjective, then TT* is invertible and T† =T"(TT*)-!.
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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