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(b) Let B = {₁,...,n} be a basis for an inner product space V with inner product (,). We can nxn matrix G by gij = (bi, b) for all i, j = 1,...,n I Prove that (7,ÿ) = [] G[y]в for all ≈, y ≤ V. 1

(b) Let B = {₁,...,n} be a basis for an inner product space V with inner product (,). We can nxn matrix G by gij = (bi, b) for all i, j = 1,...,n I Prove that (7,ÿ) = [] G[y]в for all ≈, y ≤ V. 1

Elementary Linear Algebra (MindTap Course List)
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 17E: Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner...
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(a) Let V be an inner product space with inner product (,), and let 1,...n, EV. Use proof by induction to show that n n =Σ(ti, ÿ) i=1 i=1 (b) Let B = {₁,..., bn} be a basis for an inner product space V with inner product (, ). We can define an nxn matrix G by gij = (bi, b) for all i, j = 1,..., n Prove that (,) = []G[y]B for all , y € V. 1
Transcribed Image Text:(a) Let V be an inner product space with inner product (,), and let 1,...n, EV. Use proof by induction to show that n n =Σ(ti, ÿ) i=1 i=1 (b) Let B = {₁,..., bn} be a basis for an inner product space V with inner product (, ). We can define an nxn matrix G by gij = (bi, b) for all i, j = 1,..., n Prove that (,) = []G[y]B for all , y € V. 1
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