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4 | grammer | ||
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It is easy to show that similarity in matrices is an equivalence relation (two matrices A and B of same size being similar if there exists a matrix P such that B = PAP^(-1) ) Moreover, given a matrix, its equivalence class can be finite. E.g. The equivalence of nxn matrices containing the identity matrix I is singleton (i.e. it contains only the identity matrix itself). But I do not know how many equivalence classes there are for matrices of a given size. Thanks in advance for any comment. |
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Post Closed as "too localized" by Mariano Suárez-Alvarez, Harald Hanche-Olsen, Robin Chapman, Harry Gindi, Qiaochu Yuan
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3 | added 1 characters in body | ||
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It is to show that similarity in matrices is an equivalence relation (two matrices A and B of same size being similar if there exists a matrix P such that A+ B = PAP^(-1) ) Moreover, given a matrix, its equivalence class can be finite. E.g. The equivalence of nxn matrices containing the identity matrix I is singleton (i.e. it contains only the identity matrix itself). But I do not know how many equivalence classes there are for matrices of a given size. Thanks in advance for any comment. |
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