Suppose W₁, W₂ are subspaces of a finite-dimensional inner product space. Prove the following: (a) (W₁ + W₂)+ = WW₂; (b) (W₁W₂) = W²₁² + W²₂².
Suppose W₁, W₂ are subspaces of a finite-dimensional inner product space. Prove the following: (a) (W₁ + W₂)+ = WW₂; (b) (W₁W₂) = W²₁² + W²₂².
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose W₁, W₂ are subspaces of a finite-dimensional inner product space. Prove the
following:
(a) (W₁ + W₂)+ = WW₂;
(b) (W₁ W₂)¹ = W²₁² + W²₂².
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