Given a complex matrix A follows: 1 + i 4 A = 6 1-i Questions: a. Check whether matrix A is Hermitian matrix? b. Determine the characteristic values along with the characteristic vectors of the pair? c. Through the relationship AP = PD, where D is the diagonal matrix, determine the unitary matrix P that diagonalizes A? d. Write down the diagonal matrix D referred to (show that D = P*AP)?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 9AEXP
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Given a complex matrix A follows:
6 1+i
1-i
4
A =
Questions:
a. Check whether matrix A is Hermitian matrix?
b. Determine the characteristic values along with the characteristic vectors of the pair?
c. Through the relationship AP = PD, where D is the diagonal matrix, determine the unitary matrix P that
diagonalizes A?
d. Write down the diagonal matrix D referred to (show that D = P*AP)?
Transcribed Image Text:Given a complex matrix A follows: 6 1+i 1-i 4 A = Questions: a. Check whether matrix A is Hermitian matrix? b. Determine the characteristic values along with the characteristic vectors of the pair? c. Through the relationship AP = PD, where D is the diagonal matrix, determine the unitary matrix P that diagonalizes A? d. Write down the diagonal matrix D referred to (show that D = P*AP)?
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