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What are the necessary and sufficient conditions for a matrix to be similar to B? AB is an arbitrary matrix. It is not specified that AB is a real symmetric matrix or diagonalizable. If necessary, it can be regarded as a part of the necessary and sufficient conditions
1. The definition of similarity is: for n-order square matrices A and B, if there is an invertible matrix P such that P ^ (- 1) AP = B, then a and B are similar. 2. From the definition, the simplest necessary and sufficient condition is: for a given a and B, we can find such a p such that P ^ (- 1) AP = B; or we can find a matrix C such that a and B are homogeneous
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- 3. If a and B are real symmetric matrices, it is necessary and sufficient that a and B have the same eigenvalues. Why?
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