(Difficulty: *) Consider an orthogonal basis {0:};=0..N-1 for RN. Select the statements that hold for any vector x E RN N-1 ||x|| = (x, p:)|² if and only if ||o:||2 = 1 Vi. %3D i=0 N-1 i=0 N-1 1 || |} i=0 if and only if ||oi||2 = P vi. N-1 1 ||x||} = (x, p:) |² if and only if ||Þ:|} = P vi. P i=0 ||
(Difficulty: *) Consider an orthogonal basis {0:};=0..N-1 for RN. Select the statements that hold for any vector x E RN N-1 ||x|| = (x, p:)|² if and only if ||o:||2 = 1 Vi. %3D i=0 N-1 i=0 N-1 1 || |} i=0 if and only if ||oi||2 = P vi. N-1 1 ||x||} = (x, p:) |² if and only if ||Þ:|} = P vi. P i=0 ||
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.3: Orthonormal Bases:gram-schmidt Process
Problem 71E
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