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After studying linear algebra I want to study some more concrete theories about matrix theory. I am looking for a textbook containing the following subjects:

  1. Detailed and theoretical treatment on SVD.

  2. Coprime factorization.

  3. Kronecker product

  4. Matrix calculus

  5. Maybe some important examples of matrix equations and matrix differential equations

or other important theories and applications that I missed in this list.

It's preferably on the graduate level, or advanced undergrad level, if possible with a focus on the application in control systems. I googled a lot but cannot find a suitable one. Thanks for any help!

3 Answers3

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I would also add to Three's suggestion (that is a book worth having), the books:

  • Matrix Analysis, Roger A. Horn, Charles R. Johnson
  • Topics in Matrix Analysis, Roger A. Horn, Charles R. Johnson
  • Matrix Analysis (Graduate Texts in Mathematics), Rajendra Bhatia
  • Applied Linear Algebra and Matrix Analysis (Undergraduate Texts in Mathematics), Thomas S. Shores
  • Linear Algebra Through Geometry, Thomas Banchoff and John Wermer

I think you can peruse these at your favorite book purchasing site.

You might also need some books on numerical matrix calculations for some of the items you mentioned.

Lastly, you should peruse your local college library for items that specifically interest you.

Amzoti
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This book was recommended to me:

Matrix Computations by Golub and Van Loan

It is very good and treats many of the topics you mentioned.

Artem
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Three
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Here is my suggestion: Matrix Analysis for Scientists and Engineers This is a beginning graduate level book on concrete matrix computations. The book is concise, written good (for my taste) and covers most of your requested topics. It does not have 100% of proofs of the results, but most of the topics given good theoretical treatment.

Artem
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