The trace of any power of a nilpotent matrix is zero.
2.
One example of a nilpotent element is a nilpotent matrix.
3.
Where D is a diagonal matrix and N is a nilpotent matrix.
4.
The trace of a nilpotent matrix is zero.
5.
Thus, a linear map is nilpotent iff it has a nilpotent matrix in some basis.
6.
:This is a nilpotent matrix.
7.
This series in general does not converge for every matrix " K ", as it would not for any real number with absolute value greater than unity, however, this particular " K " is a nilpotent matrix, so the series actually has a finite number of terms ( " K " " m " is zero if " m " is the dimension of " K " ).
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