What is "main diagonal"

n. (context linear algebra English) The (imagined) diagonal line from the top left to the bottom right of a square matrix.

n. the diagonal of a square matrix running from the upper left entry to the lower right entry [syn: principal 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 where i = j. All off-diagonal elements are zero. 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 such that i + j = N − 1. That is, it runs from the top right corner to the bottom left corner:

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