In
linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as:
:a_1x_1+\cdots +a_nx_n=b,
linear maps such as:
:(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n,
and their representations in vector spaces and through matrice ...
, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, major diagonal, or good diagonal) of a
matrix
Matrix most commonly refers to:
* ''The Matrix'' (franchise), an American media franchise
** '' The Matrix'', a 1999 science-fiction action film
** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchi ...
is the list of entries
where
. All
off-diagonal elements are
zero
0 (zero) is a number representing an empty quantity. In place-value notation such as the Hindu–Arabic numeral system, 0 also serves as a placeholder numerical digit, which works by Multiplication, multiplying digits to the left of 0 by th ...
in a
diagonal matrix. The following four matrices have their main diagonals indicated by red ones:
:
Antidiagonal
The antidiagonal (sometimes counter diagonal, secondary diagonal, trailing diagonal, minor diagonal, off diagonal, or bad diagonal) of an order
square matrix
In mathematics, a square matrix is a matrix with the same number of rows and columns. An ''n''-by-''n'' matrix is known as a square matrix of order Any two square matrices of the same order can be added and multiplied.
Square matrices are often ...
is the collection of entries
such that
for all
. That is, it runs from the top right corner to the bottom left corner.
:
See also
*
Trace
References
* {{MathWorld, id=Diagonal, title=Main diagonal
Matrices