invertible matrix

English

Noun

invertible matrix (plural invertible matrices)

1. (linear algebra) Any 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.

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

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

   • 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:

     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.

Antonyms

• singular matrix
• degenerate matrix

Hyponyms

• unitary matrix

Translations

square matrix which, when multiplied by some other, yields the identity matrix

• Finnish: kääntyvä matriisi
• German: invertierbare Matrix f, reguläre Matrix f
• Hungarian: invertálható mátrix (hu)
• Italian: matrice invertibile f
• Japanese: 正則行列 (ja) (seisoku gyōretsu)
• Polish: macierz odwrotna f
• Romanian: matrice inversabilă f
• Swedish: inverterbar matris c

Further reading

• Generalized inverse on Wikipedia.Wikipedia
• Binomial inverse theorem on Wikipedia.Wikipedia
• Matrix decomposition on Wikipedia.Wikipedia
• Square root of a matrix on Wikipedia.Wikipedia