Category:Definitions/Diagonally Dominant Matrices

This category contains definitions related to Diagonally Dominant Matrices.
Related results can be found in Category:Diagonally Dominant Matrices.

Let $\mathbf A$ be a square matrix.

By Rows

$\mathbf A$ is diagonally dominant by rows if and only if:

in each row of $\mathbf A$, the absolute value of the element on the main diagonal is greater than the sum of the absolute values of the other elements on that row.

By Columns

$\mathbf A$ is diagonally dominant by columns if and only if:

in each column of $\mathbf A$, the absolute value of the element on the main diagonal is greater than the sum of the absolute values of the other elements in that column.

That is, if its transpose is diagonally dominant by rows.