In mathematics, particularly linear algebra, a zero matrix or null matrix is a matrix with all its entries being zero. Some examples of zero matrices are
The set of m×n matrices with entries in a ring K forms a ring
The zero matrix is the additive identity in
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.