Page "Trace (linear algebra)" Paragraph 9

Assume the characteristic of the field is zero.

Then the trace of the identity matrix is the dimension of the space ; this leads to generalizations of dimension using trace.

The trace of a projection ( i. e., P < sup > 2 </ sup > = P ) is the rank of the projection.

The trace of a nilpotent matrix is zero.

The product of a symmetric matrix and a skew-symmetric matrix has zero trace.