Nilpotent matrix (source code)

= Nilpotent matrix
{title2=$A^k=0$}
{wiki}

A square <matrix> is nilpotent when one of its positive powers is zero. It represents a <nilpotent linear map> in a chosen basis; changing basis preserves nilpotence. Over an algebraically closed field, its <Jordan normal form> has only zero-eigenvalue blocks.