# Trace of a square matrix

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

The sum of the entries on the main diagonal of this matrix. The trace of a matrix is denoted by , or :

Let be a square matrix of order over a field . The trace of coincides with the sum of the roots of the characteristic polynomial of . If is a field of characteristic 0, then the traces uniquely determine the characteristic polynomial of . In particular, is nilpotent if and only if for all .

If and are square matrices of the same order over , and , then

while if ,

The trace of the tensor (Kronecker) product of square matrices over a field is equal to the product of the traces of the factors.