In order to complete the previous post on unitary matrix decomposition (sum) , I give here two interesting links about other known matrix decomposition :
- http://en.wikipedia.org/wiki/Matrix_decomposition
- http://www.ece.northwestern.edu/~mya671/files/Matrix_YM_.pdf
In quantum physics we love to use unitary operations, so here are the decompositions involving unitary matrices. We have U,V unitary, T,R triangular, Q orthogonal and D diagonal :
- Schur Decomposition : $$M=UTU^{\dagger}$$
- Singular Value Decomposition : $$ M=UDV^{*}$$
- QZ decomposition (generalized Schurr) : $$M = UTV^*$$
- QR decomposition : $$M=QR$$
Do you use other useful unitary decomposition?