trace
The trace of a square matrix is defined to be the sum of the diagonal entries of . It satisfies the following formulas:
- •
- •
()
where and are square matrices of the same size.
The trace of a linear transformation from any finite dimensional vector space to itself is defined to be the trace of any matrix representation of with respect to a basis of . This scalar is independent of the choice of basis of , and in fact is equal to the sum of the eigenvalues
of (over a splitting field
of the characteristic polynomial
), including multiplicities.
The following link presents some examples for calculating the trace of a matrix.
A trace on a -algebra is a positive linear functional that has the .