invertible matrix en · NOUN
Meanings
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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).
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: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 199:1975 [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.
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| invertible matrices | Number=Plur | lexicographic |
Antonyms
singular matrix · degenerate matrix
Hyponyms
Translations (9)
de invertierbare Matrix (square matrix which, when multiplied by some other, yields the identity matrix) · fi kääntyvä matriisi (square matrix which, when multiplied by some other, yields the identity matrix) · sv inverterbar matris (square matrix which, when multiplied by some other, yields the identity matrix) · it matrice invertibile (square matrix which, when multiplied by some other, yields the identity matrix) · de reguläre Matrix (square matrix which, when multiplied by some other, yields the identity matrix) · ro matrice inversabilă (square matrix which, when multiplied by some other, yields the identity matrix) · ja 正則行列 (square matrix which, when multiplied by some other, yields the identity matrix) · pl macierz odwrotna (square matrix which, when multiplied by some other, yields the identity matrix) · hu invertálható mátrix (square matrix which, when multiplied by some other, yields the identity matrix)