If a and B are real symmetric matrices, it is necessary and sufficient that a and B have the same eigenvalues. Why?
It is a theorem that similar matrices have the same eigenvalues
On the contrary, because a and B are real symmetric matrices, a can be diagonalized, that is, a and B are similar to the same diagonal matrix composed of eigenvalues, so a and B are similar
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- 2. 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?
- 3. 1. How to judge whether a matrix is similar to a diagonal matrix? 2. What kind of matrix is diagonal?
- 4. A necessary and sufficient condition for diagonal matrix Excuse me? Why is it necessary and sufficient for a diagonal matrix to be both an upper triangular matrix and a lower triangular matrix?
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- 16. If two matrices are similar, can they be diagonalized? In other words, can diagonalize the matrix and its similar matrix? Best examples
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- 19. The sufficient condition for the similarity of n-order matrix A and diagonal matrix is that a has n different eigenvalues and a is a real symmetric matrix. I want to ask: the general problem is to prove that n-order matrix A and B are similar. In this way, is it necessary to prove matrix B first It can be diagonalized, and then the above sufficient conditions are used to prove the similarity
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