Out of the unit matrix and a real non-invertible symmetric matrix of the same size,(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\delta_{ij}[/tex] and [tex]M_{ij}[/tex]

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

[tex]A_{ij} B_{jk}=0,[/tex] and [tex]A_{ij} A_{jk}=B_{ij} B_{jk}=\delta_{ik}[/tex]

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

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# Projection matrices

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