Main diagonal

In linear algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, or major diagonal) of a matrix $A$ is the collection of entries $A_{i,j}$ where $i = j$. The following three matrices have their main diagonals indicated by red 1's:

$\begin{bmatrix} \color{red}{1} & 0 & 0\\ 0 & \color{red}{1} & 0\\ 0 & 0 & \color{red}{1}\end{bmatrix} \qquad \begin{bmatrix} \color{red}{1} & 0 & 0 & 0 \\ 0 & \color{red}{1} & 0 & 0 \\ 0 & 0 & \color{red}{1} & 0 \end{bmatrix} \qquad \begin{bmatrix} \color{red}{1} & 0 & 0\\ 0 & \color{red}{1} & 0\\ 0 & 0 & \color{red}{1}\\ 0 & 0 & 0\end{bmatrix}$

The antidiagonal (sometimes counterdiagonal, secondary diagonal, trailing diagonal or minor diagonal) of a dimension $N$ square matrix, $B$, is the collection of entries $B_{i,j}$ such that $i + j = N - 1$. That is, it runs from the top right corner to the bottom left corner:

$\begin{bmatrix} 0 & 0 & \color{red}{1}\\ 0 & \color{red}{1} & 0\\ \color{red}{1} & 0 & 0\end{bmatrix}$

See also

• Diagonal matrix
• Trace
• Anti-diagonal matrix

References

• Weisstein, Eric W., "Main diagonal", MathWorld.