An operator T: IR" → IR" is called a self-adjoint operator if [T]®p is a symmetric matrix, where B is an orthonormal basis of IR". Decide whether the below operator is self- adjoint. Justify! T: IR³ → IR³3 (x, y, z) → (x+D·y +U · z, -D . x + M · y + 4z, U · x + 4y + 32) Where: D= 0; U= 8; M=5.
An operator T: IR" → IR" is called a self-adjoint operator if [T]®p is a symmetric matrix, where B is an orthonormal basis of IR". Decide whether the below operator is self- adjoint. Justify! T: IR³ → IR³3 (x, y, z) → (x+D·y +U · z, -D . x + M · y + 4z, U · x + 4y + 32) Where: D= 0; U= 8; M=5.
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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![An operator T : IR" → IRª is called a self-adjoint operator if [T]B is a symmetric matrix,
where B is an orthonormal basis of IR". Decide whether the below operator is self-
adjoint. Justify!
T: IR3 → IR³
(x, y, z) •
H (x + D. y +U · z, –D · x+M·y + 4z, U · x + 4y + 3z)
|
Where: D= 0; U= 8; M=5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f3f050e-4f1e-425f-becb-0b3efdabc424%2Ff2a1c2fc-2d81-40f3-86f5-78a9d38965b9%2Fegprg6a_processed.png&w=3840&q=75)
Transcribed Image Text:An operator T : IR" → IRª is called a self-adjoint operator if [T]B is a symmetric matrix,
where B is an orthonormal basis of IR". Decide whether the below operator is self-
adjoint. Justify!
T: IR3 → IR³
(x, y, z) •
H (x + D. y +U · z, –D · x+M·y + 4z, U · x + 4y + 3z)
|
Where: D= 0; U= 8; M=5.
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