How to find similar matrices

My lecture notes write that two matrices are said to be similar if there exists an n × n invertible matrix P such that B = P − 1 A P.


Determine Whether Given Matrices are Similar

This is essentially because for such small matrices the characteristic polynomial leaves very little room for variation of the minimal polynomial (and other invariant factors that

Similar Matrices -

If matrices A and B are similar, matrix B can be found by applying elementary operations on the rows of matrix A, and vice versa. Obviously, the similarity between matrices is a reflective operation. That is, if A is similar to B, B is also similar to A. Furthermore, the similarity of matrices is also symmetric. See more

Similar Matrices

Similar matrices represent the same linear operator with respect to different bases (this is the motivation for the notion of similarity), and so naturally such matrices must have

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matrix A. So, both A and B are similar to A, and therefore A is similar to B. However, if two matrices have the same repeated eigenvalues they may not be distinct. For example, the zero

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Similar matrices

People often ask: How do we show that two matrices are similar? We know that two similar matrices and have the same eigenvalues. Therefore, if and do not have the same eigenvalues