As the unitary group does not contain the zero matrix, this action is free.

Hence the examples above represent zero matrices over any ring.

The identity matrix I and any square zero matrix are diagonal.

The zero matrix is the additive identity in .

The pseudoinverse of a zero matrix is its transpose.

The adjacency matrix of an empty graph is a zero matrix.

For the zero matrix and the identity matrix, the spread is zero.

The columns having zero matrix elements, corresponding to dangling nodes, are replaced by a constant value 1/N.

Here is a square right triangular matrix, and the zero matrix has dimension .

The only nilpotent diagonalizable matrix is the zero matrix.

Only a zero matrix has rank zero.

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

In mathematics, particularly linear algebra, a zero matrix is a matrix with all its entries being zero.

It is always particularly significant if a block is the zero matrix; that carries the information that a summand maps into a sub-sum.

If the latter holds, then the solution is unique if and only if A has full column rank, in which case is a zero matrix.

This is either a 1x1 zero matrix, or an affine Cartan matrix, whose Dynkin diagram is given.

By using the fully swept moment matrix, we represent the vacuous linear belief functions as a zero matrix in the swept form follows:

Examples include binary matrices, the zero matrix, the unit matrix, and the adjacency matrices used in graph theory, amongst many others.

Note that the exponential map is a local diffeomorphism between a neighborhood U of the zero matrix and a neighborhood V of the identity matrix .

Therefore, the configuration where all the lights are out is the Zero matrix and the configuration where all the lights are on is a matrix where every entry is a 1.

A block diagonal matrix is a block matrix which is a square matrix, and having main diagonal blocks square matrices, such that the off-diagonal blocks are zero matrices.

This weak inequality holds with equality if and only if for any vector w; this provides an infinitude of minimizing solutions unless A has full column rank, in which case is a zero matrix.

There is exactly one zero matrix of any given size mxn having entries in a given ring, so when the context is clear one often refers to the zero matrix.

A useful property of the sub- and superdiagonal matrices used in the construction is that both are nilpotent; that is, when raised to a sufficiently high integer power, they degenerate into the zero matrix.

The Cayley-Hamilton theorem states that substituting the matrix 'A' in the characteristic polynomial (which involves multiplying its constant term by 'In', since that is the zeroth power of 'A') results in the zero matrix: