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Thread: Similar matrices

  1. #1
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    Similar matrices

    Given two matrices A and B that are similar, what is the procedure for finding the change of basis matrix, S with

    $\displaystyle A=SBS^{-1}$

    Thank you in advance.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    If $\displaystyle A,B\in \mathbb{K}^{n\times n}$ are similar matrices, there is a method for finding $\displaystyle S$ in a finite number of elemental transformations using the concept of equivalence of $\displaystyle \lambda$ matrices.

    Another way is to use the fact that $\displaystyle A,B$ have the same Jordan canonical form, etc. All of this would depend on your previous theoretical knowledge.


    Fernando Revilla
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