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I am looking for a good collection of facts regarding the various types of matrix factorizations, something like a "Handbook of Matrix Factorizations" or a very-thorough review paper. I am hoping for a cohesive collection which talks about many different types of matrix factorizations, under which conditions can they be done, their properties, and their connections with one another (such as the connection between the eigenvalue decomposition, the singular value decomposition, and the polar decomposition).

The various books I have looked at are

as well as many different articles on Wikipedia and MathWorld. This page on Wikipedia comes very close but I don't like it for two reasons. The information is very fragmented on different pages/links and I want something more reliable, something that's been peer-reviewed or written/edited by an acknowledged expert. The "Handbook of Linear Algebra" also comes close but not as many factorizations as I would like. I would like to learn about other factorizations besides your standard LU, QR, EVD, and SVD, such as the polar decomposition or Mostow's decomposition. Bonus points for something that includes approximations such as the various low-rank approximations.

Maybe this doesn't exist, but

does anyone know of a good reference on different types of matrix factorizations?

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The canonical references for such topics are the two books by Horn and Johnson

Horn, Roger A.; Johnson, Charles R., Matrix analysis, Cambridge etc.: Cambridge University Press. XIII, 561 p. £ 35.00 (1985). ZBL0576.15001.

Horn, Roger A.; Johnson, Charles R., Topics in matrix analysis, Cambridge etc.: Cambridge University Press. viii, 607 p. £ 45.00; $ 59.50 (1991). ZBL0729.15001.

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