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#### Petrus

##### Well-known member

- Feb 21, 2013

- 739

"Can we construct a \(\displaystyle 4x4\) Matrix \(\displaystyle B\) so that rank \(\displaystyle B=4\) but rank \(\displaystyle B^2=3\)"

My thought:

we got one condition for this to work is that det \(\displaystyle B=0\) and det \(\displaystyle B^2 \neq 0\) and B also have to be a upper/lower or identity Matrix. And this Will not work.. I am wrong or can I explain this in a better way?

Regards,

\(\displaystyle |\pi\rangle\)