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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F75a69a56-1d07-4e8b-b859-b86f72adb8cb%2F32605188-fd04-49ac-9d1e-328900e9d7dc%2Fo88d4i7_processed.png&w=3840&q=75)
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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