En álgebra lineal, una matriz diagonal es una matriz cuadrada en que las entradas son todas nulas salvo en la diagonal principal, y éstas pueden ser nulas o no. Así, la matriz D = (di,j) es diagonal si: Ejemplo: Toda matriz diagonal es también una matriz simétrica, triangular (superior e inferior) y (si las entradas provienen del cuerpo R o C) normal. Otro ejemplo de matriz diagonal es la matriz identidad.

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In linear algebra, a diagonal matrix is a matrix (usually a square matrix) in which the off-diagonal elements (entries not on the main diagonal) are all zero. The main diagonal entries themselves may or may not be zero. Thus, the matrix D = (di,j) with n columns and n rows is diagonal if: For example, the following matrix is diagonal: The term diagonal matrix may sometimes refer to a rectangular diagonal matrix, which is an m-by-n matrix with all the entries not of the form di,i being zero. For example: or However, in the remainder of this article we will consider only square matrices. Any square diagonal matrix is also a symmetric matrix. Also, if the entries come from the field R or C, then it is a normal matrix as well. Equivalently, we can define a diagonal matrix as a matrix that is both upper- and lower-triangular. The identity matrix In and any square zero matrix are diagonal. A one-dimensional matrix is always diagonal.

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