Diagonally Dominant Matrix - Examples

Examples

The matrix

\mathbf A = \begin{bmatrix} 3 & -2 & 1\\ 1 & -3 & 2\\ -1 & 2 & 4\end{bmatrix}

gives

since
since
since .

Because the magnitude of each diagonal element is greater than or equal to the sum of the magnitude of other elements in the row, A is diagonally dominant.

The matrix

\mathbf B = \begin{bmatrix} -2 & 2 & 1\\ 1 & 3 & 2\\ 1 & -2 & 0\end{bmatrix}

But here,

since
since
since .

Because and are less than the sum of the magnitude of other elements in their respective row, B is not diagonally dominant.

The matrix

\mathbf C = \begin{bmatrix} -4 & 2 & 1\\ 1 & 6 & 2\\ 1 & -2 & 5\end{bmatrix}

gives

since
since
since .

Because the magnitude of each diagonal element is greater than the sum of the magnitude of the other elements in the row, C is strictly diagonally dominant.

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