Splitting an Indefinite Matrix into 2 definite matrices I'm attempting to use some quadratic programming techniques to solve a particular optimization problem and my chosen Objective Function is indefinite.
I've found some texts online which regard splitting the objective function into two components of which one is positive semi-definite and one is negative semi-definite.
All these concerns aside, my question becomes this:
If an nxn matrix Q is indefinite, is there an algorithm which produces matrices A, and B, both nxn such that A and B are both positive semidefinite and Q = A - B?
Thanks,
James

You can just set $A = Q + kI$ where $k$ is larger than all the negative eigenvalues of $Q$, and put $B = kI$.
