What is the meaning and definition of equivalence of two matrices? What is the relationship between equivalence and similarity of two matrices? What are the necessary and sufficient conditions for equivalence of two matrices? What are the properties of equivalence?

A is equal to B by a series of elementary transformations. That is to say, if there is an invertible matrix PQ such that B = PAQ, then the rank of AB is equal. And ab similarity is that there is an invertible matrix P such that B = p-1ap. Therefore, the conclusion of similarity is stronger than equivalence and has more properties. For example, the eigenvalues and determinants are the same

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