(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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Solve b
![(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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09caa562-c0c8-4a11-85df-abb5e549e1a9%2F1b24453b-9786-4f7b-ab90-91f5d9d9767b%2Fze2s9qb_processed.jpeg&w=3840&q=75)
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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