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  2. Moore–Penrose inverse - Wikipedia

    en.wikipedia.org/wiki/Moore–Penrose_inverse

    The Octave programming language provides a pseudoinverse through the standard package function pinv and the pseudo_inverse() method. In Julia (programming language), the LinearAlgebra package of the standard library provides an implementation of the Moore–Penrose inverse pinv() implemented via singular-value decomposition. [25]

  3. Block matrix pseudoinverse - Wikipedia

    en.wikipedia.org/wiki/Block_matrix_pseudoinverse

    Instead of ([] []), we need to calculate directly or indirectly [citation needed] [original research? (), (), (), ().In a dense and small system, we can use singular value decomposition, QR decomposition, or Cholesky decomposition to replace the matrix inversions with numerical routines.

  4. Zero-forcing precoding - Wikipedia

    en.wikipedia.org/wiki/Zero-forcing_precoding

    When the channel state information is perfectly known at the transmitter, the zero-forcing precoder is given by the pseudo-inverse of the channel matrix. Zero-forcing has been used in LTE mobile networks. [2]

  5. Constrained generalized inverse - Wikipedia

    en.wikipedia.org/.../Constrained_generalized_inverse

    So, a generalized inverse of () is also called a -constrained pseudoinverse of . An example of a pseudoinverse that can be used for the solution of a constrained problem is the Bott–Duffin inverse of constrained to , which is defined by the equation

  6. Generalized inverse - Wikipedia

    en.wikipedia.org/wiki/Generalized_inverse

    In mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element x is an element y that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of ...

  7. Woodbury matrix identity - Wikipedia

    en.wikipedia.org/wiki/Woodbury_matrix_identity

    A common case is finding the inverse of a low-rank update A + UCV of A (where U only has a few columns and V only a few rows), or finding an approximation of the inverse of the matrix A + B where the matrix B can be approximated by a low-rank matrix UCV, for example using the singular value decomposition.

  8. Pseudoinverse - Wikipedia

    en.wikipedia.org/?title=Pseudoinverse&redirect=no

    This page was last edited on 20 August 2008, at 19:14 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may ...

  9. Pseudo-differential operator - Wikipedia

    en.wikipedia.org/wiki/Pseudo-differential_operator

    The adjoint and transpose of a pseudo-differential operator is a pseudo-differential operator. If a differential operator of order m is (uniformly) elliptic (of order m) and invertible, then its inverse is a pseudo-differential operator of order −m, and its symbol can be calculated. This means that one can solve linear elliptic differential ...