Main Matrix Diagonal

A Main Matrix Diagonal is a vector from a matrix [math]\displaystyle{ A }[/math] is the collection of entries [math]\displaystyle{ A_{i,j} }[/math] where [math]\displaystyle{ i = j }[/math].

• AKA: Principal Diagonal.
• See: Linear Algebra, Identity Matrix, Symmetric Matrix.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/main_diagonal Retrieved:2015-2-16.
  • In linear algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, or major diagonal) of a matrix [math]\displaystyle{ A }[/math] is the collection of entries [math]\displaystyle{ A_{i,j} }[/math] where [math]\displaystyle{ i = j }[/math]. The following three matrices have their main diagonals indicated by red 1's: :[math]\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} }[/math] The antidiagonal (sometimes counterdiagonal, secondary diagonal, or minor diagonal) of a dimension [math]\displaystyle{ N }[/math] square matrix, [math]\displaystyle{ B }[/math], is the collection of entries [math]\displaystyle{ B_{i,j} }[/math] such that [math]\displaystyle{ i j = N 1 }[/math]. That is, it runs from the top right corner to the bottom left corner: :[math]\displaystyle{ \begin{bmatrix} 0 & 0 & \color{red}{1} \\ 0 & \color{red}{1} & 0 \\ \lt P\gt \color{red}{1} & 0 & 0\end{bmatrix} }[/math]

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