Main diagonal

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

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

Antidiagonal

See also: Anti-diagonal matrix

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

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

See also

• Trace

References

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