are all nilpotent matrices singular?

if so, how is that possible?

cheers

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- Mar 30th 2008, 02:13 AMthe wildcatnilpotent matrices
are all nilpotent matrices singular?

if so, how is that possible?

cheers - Mar 30th 2008, 03:16 AMmr fantastic
Yes.

I quote from Nilpotent matrix - Wikipedia, the free encyclopedia:

"Over an algebraically closed field, a matrix M is nilpotent if and only if its eigenvalues are all zero. Therefore the determinant and trace of M are both zero, and nilpotent matrices are not invertible."