Matrix Singularity

A rectangular matrix of values (e.g., a sums of squares and cross-products matrix) is singular if the elements in a column (or row) of the matrix are linearly dependent on the elements in one or more other columns (or rows) of the matrix. For example, if the elements in one column of a matrix are 1, -1, 0, and the elements in another column of the matrix are 2, -2, 0, then the matrix is singular because 2 times each of the elements in the first column is equal to each of the respective elements in the second column. Such matrices are also said to suffer from multicollinearity problems, since one or more columns are linearly related to each other.

A unique, regular matrix inverse cannot be computed for singular matrices, but generalized inverses (an infinite number of them) can be computed for any singular matrix.

See also: matrix inverse.