invertible matrix

invertible matrix

  1. (linear algebra) An n×n square matrix for which some other such matrix exists such that when they 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, 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 Translations
  • Italian: matrice invertibile

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