invertible matrix

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Noun

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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.

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