If the system has a singular matrix then there is a solution set with an infinite number of solutions.

Give an example of a 3x3 singular matrix whose cofactors are all nonzero.

Every singular matrix can be written as a product of nilpotent matrices.

Singular matrices can also be factored, but not uniquely.

Note that this range does not include the values for , as this leads to a singular matrix, which can't be solved.

For massless particles, the term is replaced by a singular matrix that obeys the relations and .

It should be noted that [a] is a singular matrix where a is its (right and left) null-vector.

A zero determinant indicates a singular matrix, which means that at least one of the predictors is a linear function of one or more others.

This is true because singular matrices are the roots of the polynomial function in the entries of the matrix given by the determinant.

Note that in Car Robots, there is not one singular Matrix, but multiple ones, each held by a high-ranking Autobot.

Equivalently, the set of singular matrices is closed and nowhere dense in the space of n-by-n matrices.

Singular matrices are rare in the sense that a square matrix randomly selected from a continuous uniform distribution on its entries will almost never be singular.

Note: The list of codes should not be exhaustive, i.e. all existing codes should not be listed or else a singular matrix will result.

Notice that the set of orthogonal matrices can be viewed as consisting of two manifolds in R separated by the set of singular matrices.

If is a singular matrix of rank , then it admits an LU factorization if the first leading principal minors are nonsingular, although the converse is not true.

Singular matrices can be factorised as the product of two rectangular matrices - again, in more ways than one - the orders of which are determined by the rank of the matrix.

From this point of view, we can define the pseudo-determinant for a singular matrix to be the product of its nonzero eigenvalues (the density of multivariate normal distribution will need this quantity).

The QR decomposition can be used in a preparation step to reduce a singular matrix A to a smaller regular matrix, and inside every step to speed up the computation of the inverse.

We present a nontrivial family of non-Abelian Toda lattice motions that can be specialized to ones that are not finite, but not infinitely extendible either, as they contain nonvanishing but singular matrices of rank (n – s).

Vol'pert developed an effective algorithm for calculating the index of an elliptic problem before the Atiyah-Singer index theorem appeared: He was also the first to show that the index of a singular matrix operator can be different from zero.