b) If the matrix has an A = PDPT, prove that A is a orthogonal diagonalization šymmetric matrix

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Answer the following parts accordingly:
b) If the matrix has an orthogonal diagonalization
A= PDPT, prove that A is a šymmetric matrix
c) If ū is a (common) eigenvector of the nxn matrices
A and B, prove that ū is also an
eigenvector of AB
Transcribed Image Text:b) If the matrix has an orthogonal diagonalization A= PDPT, prove that A is a šymmetric matrix c) If ū is a (common) eigenvector of the nxn matrices A and B, prove that ū is also an eigenvector of AB
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