invertible matrix

plural invertible matrices

1. linear algebraAny n×n square matrix for which there exists a corresponding inverse matrix (i.e., a second (or possibly the same) matrix such that when the two are multiplied by each other, in either order, the result is the n×n identity matrix).

   1975 [Prentice-Hall], Kenneth Hoffman, Analysis in Euclidean Space, Dover, 2007, page 65, It says that, if A is a singular matrix, then every neighborhood of A contains an invertible matrix. In other words, if A is singular, we can perturb A just a little and obtain an invertible matrix.

   2 more examples

   There are certain very simple invertible matrices, and every invertible matrix over a field can be built up out of them.

   1997, Bernard L. Johnston, Fred Richman, Numbers and Symmetry: An Introduction to Algebra, CRC Press, page 199

   The space of real square matrices of fixed size is a vector space whose dimension is a perfect square and the invertible matrices constitute a dense open subset of this vector space.

   2013, Mahya Ghandehari, Aizhan Syzdykova, Keith F. Taylor, “A four dimensional continuous wavelet transform”, in Azita Mayeli, editor, Commutative and Noncommutative Harmonic Analysis and Applications, American Mathematical Society, page 123