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Problem 2. Given a n-order positive definite matrix 4, for any column vector x,y € R", define (x, y) = x² Ay. (1) Prove that (x, y) is an inner product in R". (11 1 (2) When n=3, A= 1 20 (103) find a set of standard orthogonal basis in the sense of

Problem 2. Given a n-order positive definite matrix 4, for any column vector x,y € R", define (x, y) = x² Ay. (1) Prove that (x, y) is an inner product in R". (11 1 (2) When n=3, A= 1 20 (103) find a set of standard orthogonal basis in the sense of

Advanced Engineering Mathematics
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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Problem 2. Given a n-order positive definite matrix A, for any column vector x, ye R", define (x, y) = x² Ay. (1) Prove that (x, y) is an inner product in R". (11 1 (2) When n=3, A-1 2 0 103) the inner product mentioned above in R". find a set of standard orthogonal basis in the sense of
Transcribed Image Text:Problem 2. Given a n-order positive definite matrix A, for any column vector x, ye R", define (x, y) = x² Ay. (1) Prove that (x, y) is an inner product in R". (11 1 (2) When n=3, A-1 2 0 103) the inner product mentioned above in R". find a set of standard orthogonal basis in the sense of
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