# Main diagonal

﻿
Main diagonal

In linear algebra, the main diagonal (sometimes leading diagonal or major diagonal or primary diagonal or principal diagonal) of a matrix A is the collection of entries Ai,j where i is equal to j.

The main diagonal of a square matrix is the diagonal which runs from the top left corner to the bottom right corner. For example, the following matrix has 1s down its main diagonal:

$\begin{bmatrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\end{bmatrix}.$

A square matrix like the above in which the entries outside the main diagonal are all zero is called a diagonal matrix. The sum of the entries on the main diagonal of a square matrix is known as the trace of that matrix.

The main diagonal of a rectangular matrix is the diagonal which runs from the top left corner and steps down and right, until the right edge or the bottom edge is reached.

$\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix}$
$\begin{bmatrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\\ 0 & 0 & 0\end{bmatrix}$

The diagonal of a square matrix from the top right to the bottom left corner is called antidiagonal, counterdiagonal, secondary diagonal, or minor diagonal.

## References

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• main diagonal — noun the diagonal of a square matrix running from the upper left entry to the lower right entry • Syn: ↑principal diagonal • Hypernyms: ↑diagonal * * * Math. See under diagonal (def. 9) …   Useful english dictionary

• main diagonal — noun The (imagined) diagonal line from the top left to the bottom right of a square matrix. Syn: leading diagonal …   Wiktionary

• main diagonal — Math. See under diagonal (def. 9). * * * …   Universalium

• Diagonal — For the avenue in Barcelona, see Avinguda Diagonal. The diagonals of a cube with side length 1. AC (shown in blue) is a space diagonal with length , while AC (shown in red) is a face diagonal and has length …   Wikipedia

• Diagonal matrix — In linear algebra, a diagonal matrix is a matrix (usually a square matrix) in which the entries outside the main diagonal (↘) are all zero. The diagonal entries themselves may or may not be zero. Thus, the matrix D = (di,j) with n columns and n… …   Wikipedia

• diagonal — diagonally, adv. /duy ag euh nl, ag nl/, adj. 1. Math. a. connecting two nonadjacent angles or vertices of a polygon or polyhedron, as a straight line. b. extending from one edge of a solid figure to an opposite edge, as a plane. 2. having an… …   Universalium

• diagonal matrix — noun A matrix in which only the entries on the main diagonal are non zero. See Also: diagonalize …   Wiktionary

• diagonal element — noun An element on the main diagonal of a square matrix, that is, an element in row k and column k where k is an integer between 1 and the number of rows (or columns) in the matrix …   Wiktionary

• diagonal matrix — noun a square matrix with all elements not on the main diagonal equal to zero • Hypernyms: ↑square matrix • Hyponyms: ↑scalar matrix …   Useful english dictionary

• Diagonal/Provença (Barcelona Metro) — Diagonal is an important station in the Barcelona metro network, named after Avinguda Diagonal, where it s located. It was originally built by TMB, and together with nearby and interconnected FGC Provença metro and commuter train station it makes …   Wikipedia