How to understand the definition of equivalence, similarity and contract matrix in line generation? 1. Equivalent matrix If the rank of a and B are equal, then a and B are equivalent, that is to say, any two matrices of the same type with the same rank pass through All elementary transformations can be transformed to be equal to each other? 2. Similarity, contract matrix How to understand the definition of p-1ap = B; p'ap = B? Why multiply an inverse matrix on the left and multiply an original matrix on the right? What's the geometry of these three relationships? --------------------------------------- No one understands? Answer as much as you know! --------------------------------------- Back to the third floor: What I want to know is about the source of the definition. --------------------------------------

How to understand the definition of equivalence, similarity and contract matrix in line generation? 1. Equivalent matrix If the rank of a and B are equal, then a and B are equivalent, that is to say, any two matrices of the same type with the same rank pass through All elementary transformations can be transformed to be equal to each other? 2. Similarity, contract matrix How to understand the definition of p-1ap = B; p'ap = B? Why multiply an inverse matrix on the left and multiply an original matrix on the right? What's the geometry of these three relationships? --------------------------------------- No one understands? Answer as much as you know! --------------------------------------- Back to the third floor: What I want to know is about the source of the definition. --------------------------------------

The definition of similarity matrix is: there is an invertible matrix P such that P (- 1) AP = B, then B is called the similarity matrix of A. reason: A is similar to B if a and B have the same eigenvalues, that is | b-ae | = | a-ae | so | b-ae | = | P (- 1) | a-ae | P | so | b-ae | = |