Page 284 - 35Linear Algebra
P. 284
284 Diagonalizing Symmetric Matrices
T
(b) Given an eigenvector of MM how can you obtain an eigenvector
T
of M M?
(c) Let
1 2
M = 3 3 .
2 1
Compute an orthonormal basis of eigenvectors for both MM T
T
and M M. If any of the eigenvalues for these two matrices agree,
choose an order for them and use it to help order your orthonor-
mal bases. Finally, change the input and output bases for the
matrix M to these ordered orthonormal bases. Comment on what
you find. (Hint: The result is called the Singular Value Decompo-
sition Theorem.)
284
