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, 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

References

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