Entries of a matrix for which the row and column indices are equal
In linear algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, major diagonal, or good diagonal) of a matrix
is the list of entries
where
. All off-diagonal elements are zero in a diagonal matrix. The following four matrices have their main diagonals indicated by red ones:
Antidiagonal[edit]
The antidiagonal (sometimes counter diagonal, secondary diagonal (*), trailing diagonal, minor diagonal, off diagonal, or bad diagonal) of an order
square matrix
is the collection of entries
such that
for all
. 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}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/377690daa5dbe71d5a1e5cf14fbdefa672895527)
(*) Secondary (as well as trailing, minor and off) diagonals very often also mean the (a.k.a. k-th) diagonals parallel to the main or principal diagonals, i.e.,
for some nonzero k =1, 2, 3, ... More generally and universally, the off diagonal elements of a matrix are all elements not on the main diagonal, i.e., with distinct indices i ≠ j.
See also[edit]
References[edit]