Main diagonal

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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, 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}

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