Let {u1, u2,..., Un} be an orthonormal basis for a subspace S of an inner product space V, and let p be the projection of v E V onto S. (a) Show that p=E-1 (v, u;) u;. (b) Show that ||p|| < ||v||.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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Let {u1, u2,..., Un} be an orthonormal basis for a subspace S of an inner product space V, and let p be
the projection of v E V onto S.
(a) Show that p E-1 (v, u;) ui.
%3D1
(b) Show that ||p|| < ||v||.
Transcribed Image Text:Let {u1, u2,..., Un} be an orthonormal basis for a subspace S of an inner product space V, and let p be the projection of v E V onto S. (a) Show that p E-1 (v, u;) ui. %3D1 (b) Show that ||p|| < ||v||.
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