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  2. Moore–Penrose inverse - Wikipedia

    en.wikipedia.org/wiki/Moore–Penrose_inverse

    In mathematics, and in particular linear algebra, the Moore–Penrose inverse ⁠ + ⁠ of a matrix ⁠ ⁠, often called the pseudoinverse, is the most widely known generalization of the inverse matrix. [1] It was independently described by E. H. Moore in 1920, [2] Arne Bjerhammar in 1951, [3] and Roger Penrose in 1955. [4]

  3. Block matrix pseudoinverse - Wikipedia

    en.wikipedia.org/wiki/Block_matrix_pseudoinverse

    In mathematics, a block matrix pseudoinverse is a formula for the pseudoinverse of a partitioned matrix. This is useful for decomposing or approximating many algorithms updating parameters in signal processing , which are based on the least squares method.

  4. 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.

  5. 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.

  6. Drazin inverse - Wikipedia

    en.wikipedia.org/wiki/Drazin_inverse

    The group inverse can be defined, equivalently, by the properties AA # A = A, A # AA # = A #, and AA # = A # A. A projection matrix P, defined as a matrix such that P 2 = P, has index 1 (or 0) and has Drazin inverse P D = P. If A is a nilpotent matrix (for example a shift matrix), then = The hyper-power sequence is

  7. Jacobi eigenvalue algorithm - Wikipedia

    en.wikipedia.org/wiki/Jacobi_eigenvalue_algorithm

    Since matrix E is orthogonal, it follows that the pseudo-inverse of S is given by + = (+). Least squares solution If matrix A {\displaystyle A} does not have full rank, there may not be a solution of the linear system A x = b {\displaystyle Ax=b} .

  8. Sherman–Morrison formula - Wikipedia

    en.wikipedia.org/wiki/Sherman–Morrison_formula

    A matrix (in this case the right-hand side of the Sherman–Morrison formula) is the inverse of a matrix (in this case +) if and only if = =. We first verify that the right hand side ( Y {\displaystyle Y} ) satisfies X Y = I {\displaystyle XY=I} .

  9. Constrained generalized inverse - Wikipedia

    en.wikipedia.org/.../Constrained_generalized_inverse

    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 ():= (+), if the inverse on the right-hand-side exists.