(a) Show that if A is a diagonalizable matrix with non-negative real eigenvalues, then there is a matrix S such that S? = A. (b) Using the general method from (a), find a matrix whose square is (1 0 8\ 0 4 0 0 0 9 A

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.4: Orthogonal Diagonalization Of Symmetric Matrices
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4. (a) Show that if A is a diagonalizable matrix with non-negative real eigenvalues,
then there is a matrix S such that S? = A.
(b) Using the general method from (a), find a matrix whose square is
1 0 8
0 4 0
0 0 9
A =
Transcribed Image Text:4. (a) Show that if A is a diagonalizable matrix with non-negative real eigenvalues, then there is a matrix S such that S? = A. (b) Using the general method from (a), find a matrix whose square is 1 0 8 0 4 0 0 0 9 A =
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