matrices, and is denoted by the symbol
followed by subscripts corresponding to the dimension of the matrix as the context sees fit.
[1][2][3] Some examples of zero matrices are The set of
is the matrix with all entries equal to
it satisfies the equation There is exactly one zero matrix of any given dimension m×n (with entries from 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 is typically denoted by 0 without any subscript indicating the parent ring.
Hence the examples above represent zero matrices over any ring.
[5] It is idempotent, meaning that when it is multiplied by itself, the result is itself.
In ordinary least squares regression, if there is a perfect fit to the data, the annihilator matrix is the zero matrix.