If you have a matrix, the "trace" of the matrix is the sum of the diagonal components of the matrix. For example, given a matrix $\mathbf{A}$:
$$\mathbf{A} = \begin{bmatrix}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix}$$
then the trace of $\mathbf{A}$ is:
$$\mathrm{trace}(\mathbf{A}) = a_{11}+a_{22}+a_{33}$$
Is there a name for the "anti-trace" which sums the off-diagonal components?
For example you could have the sum of the other diagonal across the matrix (from top right to bottom left):
$$\mathrm{some\_name}(\mathbf{A}) = a_{13}+a_{22}+a_{31}$$
Or you could have the sum of all elements of the matrix except the main diagonal elements:
$$\mathrm{some\_other\_name}(\mathbf{A}) = a_{12}+a_{13}+a_{21}+a_{23}+a_{31}+a_{32}$$
I am wondering if there is a name for these operations similar to "trace".
Thanks