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  2. Moore–Penrose inverse - Wikipedia

    en.wikipedia.org/wiki/Moore–Penrose_inverse

    The Python package NumPy provides a pseudoinverse calculation through its functions matrix.I and linalg.pinv; its pinv uses the SVD-based algorithm. SciPy adds a function scipy.linalg.pinv that uses a least-squares solver. The MASS package for R provides a calculation of the Moore–Penrose inverse through the ginv function. [24]

  3. Matrix equivalence - Wikipedia

    en.wikipedia.org/wiki/Matrix_equivalence

    In linear algebra, two rectangular m-by-n matrices A and B are called equivalent if = for some invertible n-by-n matrix P and some invertible m-by-m matrix Q.Equivalent matrices represent the same linear transformation V → W under two different choices of a pair of bases of V and W, with P and Q being the change of basis matrices in V and W respectively.

  4. Transformation matrix - Wikipedia

    en.wikipedia.org/wiki/Transformation_matrix

    In other words, the matrix of the combined transformation A followed by B is simply the product of the individual matrices. When A is an invertible matrix there is a matrix A −1 that represents a transformation that "undoes" A since its composition with A is the identity matrix. In some practical applications, inversion can be computed using ...

  5. Gaussian elimination - Wikipedia

    en.wikipedia.org/wiki/Gaussian_elimination

    A variant of Gaussian elimination called Gauss–Jordan elimination can be used for finding the inverse of a matrix, if it exists. If A is an n × n square matrix, then one can use row reduction to compute its inverse matrix, if it exists. First, the n × n identity matrix is augmented to the right of A, forming an n × 2n block matrix [A | I]

  6. Rectangular function - Wikipedia

    en.wikipedia.org/wiki/Rectangular_function

    Plot of normalized ⁡ function (i.e. ⁡ ()) with its spectral frequency components.. The unitary Fourier transforms of the rectangular function are [2] ⁡ = ⁡ = ⁡ (), using ordinary frequency f, where is the normalized form [10] of the sinc function and ⁡ = ⁡ (/) / = ⁡ (/), using angular frequency , where is the unnormalized form of the sinc function.

  7. 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 ...

  8. List of named matrices - Wikipedia

    en.wikipedia.org/wiki/List_of_named_matrices

    Matrix entries are given by the divisor function; entires of the inverse are given by the Möbius function. a ij are 1 if i divides j or if j = 1; otherwise, a ij = 0. A (0, 1)-matrix. Shift matrix: A matrix with ones on the superdiagonal or subdiagonal and zeroes elsewhere. a ij = δ i+1,j or a ij = δ i−1,j

  9. Inverse-Wishart distribution - Wikipedia

    en.wikipedia.org/wiki/Inverse-Wishart_distribution

    The Inverse Wishart distribution is a special case of the inverse matrix gamma distribution when the shape parameter = and the scale parameter =. Another generalization has been termed the generalized inverse Wishart distribution, G W − 1 {\displaystyle {\mathcal {GW}}^{-1}} .