Matrix entry ($a_{ij}$)

The matrix entry $a_{ij}$ is the value in row $i$ and column $j$ of a matrix $A$.

A matrix entry whose row and column indices differ. These entries lie outside the diagonal matrix entries. A diagonal matrix has all its off-diagonal entries equal to zero. Cancellation of these entries when averaging density matrices does not require the individual preparations to have zero entries there.

A diagonal matrix entry uses the same row and column index. The diagonal entries of a lower triangular matrix determine its determinant by their product.