Zero matrix: Information from Answers.com

This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (August 2009)

In mathematics, particularly linear algebra, a zero matrix is a matrix with all its entries being zero. Some examples of zero matrices are

$0_{1,1} = \begin{bmatrix} 0 \end{bmatrix} ,\ 0_{2,2} = \begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix} ,\ 0_{2,3} = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix} .\$

The set of m×n matrices with entries in a ring K forms a ring $K_{m,n} \,$ . The zero matrix $0_{K_{m,n}} \,$ in $K_{m,n} \,$ is the matrix with all entries equal to $0_K \,$ , where $0_K \,$ is the additive identity in K.

$0_{K_{m,n}} = \begin{bmatrix} 0_K & 0_K & \cdots & 0_K \\ 0_K & 0_K & \cdots & 0_K \\ \vdots & \vdots & & \vdots \\ 0_K & 0_K & \cdots & 0_K \end{bmatrix}_{m \times n}$

The zero matrix is the additive identity in $K_{m,n} \,$ . That is, for all $A \in K_{m,n} \,$ it satisfies

$0_{K_{m,n}}+A = A + 0_{K_{m,n}} = A.$

There is exactly one zero matrix of any given size m×n having entries in a given ring, so when the context is clear one often refers to the zero matrix. In general the zero element of a ring is unique and typically denoted as 0 without any subscript indicating the parent ring. Hence the examples above represent zero matrices over any ring.

The zero matrix represents the linear transformation sending all vectors to the zero vector.

	What is the maximum determinant in an 8 by 8 matrix of zeroes and ones? Read answer...
	What is the matrix? Read answer...
	What is a matrix? Read answer...

	How do you prove if the determinant of A is not equal to zero then the matrix A is invertible?
	Prove that a matrix a is singular if and only if it has a zero eigen value?
	C program to display zeros in diagonal of a 5 by 5 matrix?

Zero matrix

See also