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

- Golub and Van Loan's Matrix Computations
- Higham's Functions of Matrices
- Higham's Accuracy and Stability of Numerical Algorithms
- CRC Standard Mathematical Tables and Formulas
- Handbook of Linear Algebra

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?

Matrix Canonical Forms, which is a detailed-proof introduction into the more algebraic stuff (none of the forms that require real numbers to work). $\endgroup$