# Projection matrices

1. Feb 19, 2009

### TriTertButoxy

Out of the unit matrix and a real non-invertible symmetric matrix of the same size,

$$\delta_{ij}$$ and $$M_{ij}$$​

I need to build a set of projection matrices, $A_{ij}$ and $B_{ij}$ which satisfy orthonormality:

$$A_{ij} B_{jk}=0,$$ and $$A_{ij} A_{jk}=B_{ij} B_{jk}=\delta_{ik}$$​

Is this possible? or should I give up trying to find such matrices?

2. Feb 22, 2009