Category:Diagonally Dominant Matrices

This category contains results about Diagonally Dominant Matrices.
Definitions specific to this category can be found in Definitions/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.