(b) State the eigenvalues of ATA and find the eigenspace associated with each eigenvalue. Hence determine if AT A is diagonalisable.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
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part b)

 

For parts (a) to (c) of this question, we consider the 2 x 3 matrix A =
(619)
(a) Compute AT A and show that its characteristic polynomial can be factored as:
XATA(X) = X(X - 1)(A-3)
(b) State the eigenvalues of ATA and find the eigenspace associated with each eigenvalue.
Hence determine if AT A is diagonalisable.
Transcribed Image Text:For parts (a) to (c) of this question, we consider the 2 x 3 matrix A = (619) (a) Compute AT A and show that its characteristic polynomial can be factored as: XATA(X) = X(X - 1)(A-3) (b) State the eigenvalues of ATA and find the eigenspace associated with each eigenvalue. Hence determine if AT A is diagonalisable.
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