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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. All off-diagonal elements are zero in a diagonal matrix. The following three matrices have their main diagonals indicated by red 1's:

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

Antidiagonal
See also: Anti-diagonal matrix

The antidiagonal (sometimes counter diagonal, secondary diagonal, trailing diagonal, minor diagonal, or bad diagonal) of a dimension N square matrix, B {\displaystyle B} B, is the collection of entries \( B_{{i,j}} \) 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:

\( {\begin{bmatrix}0&0&\color {red}{1}\\0&\color {red}{1}&0\\\color {red}{1}&0&0\end{bmatrix}} \)

See also

Trace

Mathematics Encyclopedia

Hellenica World - Scientific Library

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