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Similarity transformation (Read 1781 times)
Gerrit-Jan Linker
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Similarity transformation
06.11.13 at 10:42:26
Similarity transformation
A matrix A and B are called similar when B = P-1AP
Matrix P-1AP is the similarity transformation of A.
Orthogonal transformation: When A is orthogonal then P-1AP is a orthogonal transformation.
Unitary transformation: When A is unitary then P-1AP is a unitary transformation.
Implications for eigen values and eigen vectors:
The eigenvalues of A and B are the same.
Each eigenvector w of B can be obtained from an eigevector v of A: w=P-1v
Note that A, B and P are matrices and v and w are vectors.
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« Last Edit: 06.11.13 at 10:51:17 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
Linker IT Software
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