Topological theory on matrices

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Can anyone suggest me a good book for matrix topology With more number of problems Thanking you

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First of all, I do not think there is a book on matrix topology (which I understand as "topology of various natural sets of matrices given by matrix equations/inequalities"), along the lines of your question: Not because there is not much to say, but since the subject is way too vast and there is no common theme to organize the material. It would be nice if somebody wrote a "cook-book" style textbook on this though (similar to "cook-books" on ODEs and PDEs). Nevertheless, what you can do is:

  1. Look at the right hand side column in this question page for answers to various questions on topology of sets of matrices.

  2. Type "topology matrices" in the search box in the upper right corner of this page. You will find 280 (!) links to MSE questions (and answers) which may serve as a good source of problems (and solutions).