Triangular matrix

[hayu601]

1. The problem statement, all variables and given/known data


I have block matrix M = [A B;
C D]

Is it always possible to get matrix U, such that the followings hold?:

1. UMU^{-1}=Triangular matrix, and

2. U = [P x;
x x ]

3. PAP^{-1}= triangular matrix

x = don't care

or in other words: can we always find matrix U that make M triangular, with its first component: matrix P that make A triangular.

Please help me, I m really stuck

thanks a lot