Suppose U and W are finite-dimensional subspaces of an inner product space V. Prove that Pʊ Pw = 0 if and only if (u, w) = 0 for all u EU and all w Є W. Hint: By the equation PuPw = 0, we mean that for any vector v Є V, PUPwv = 0.
Suppose U and W are finite-dimensional subspaces of an inner product space V. Prove that Pʊ Pw = 0 if and only if (u, w) = 0 for all u EU and all w Є W. Hint: By the equation PuPw = 0, we mean that for any vector v Є V, PUPwv = 0.
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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