Moore-Penrose inverse matrix
On polynomial EPr matrices
... MOORE-PENROSE INVERSE OF AN EP -X-MATRIX r The following theorem gives a set of necesssry and sufficient conditions for the existence of the X-matrix Moore-Penrose inverse of a given X-m[r] ...
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Applications of the Moore-Penrose Generalized Inverse to Linear Systems of Algebraic Equations
... The concept of the Moore-Penrose generalized inverse of matrix has been exploited recently in many contexts. It presents solutions for many singular problems in linear algebra, especially for ...
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An Efficient Schulz-type Method to Compute the Moore-Penrose Inverse
... the Moore-Penrose inverse of a matrix is ...of matrix multiplications and the average CPU time of our method are considerably less than those of other ...
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Testing of Hypothesis by using Generalized Inverse of Matrix
... by Moore in 1920 and autonomously rediscovered by Penrose in ...1955. Penrose demonstrated that, for each limited grid A (square or rectangular) of Real (or complex) components, ...
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A predictor corrector iterative method for solving linear least squares problems and perturbation error analysis
... the Moore–Penrose inverse of a ...inner inverse of the matrix which is the Moore–Penrose inverse of the matrix, and they provided numerical results for the ...
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Least squares Hermitian problem of complex matrix equation \((AXB,CXD)=(E,F)\)
... complex matrix equation (AXB,CXD) = (E, F) with complex arbitrary coefficient matrices A, B, C, D and the right-hand side E, ...a matrix-vector product and the Moore-Penrose generalized ...
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Least Squares Hermitian Problem of Matrix Equation (AXB, CXD) = (E, F) Associated with Indeterminate Admittance Matrices
... admittance matrix. If A is an indeterminate admittance matrix and a Hermi- tian matrix, then A is called a Hermitian indeterminate admittance ...complex matrix equation ( AXB CXD , ) ( = E F , ...
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On mixed type reverse order laws for the Moore Penrose inverse of a matrix product
... see, for example, [1]. Thus, (25) could be regarded as two new equivalent statements for the commutativity of two orthogonal projectors. There are many results in the literature on products of orthogonal projectors and ...
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Dynamic inversion of underactuated systems via squaring transformation matrix
... weighting matrix such that it does not saturate the control surface actuators ...weighting matrix is then used to form the pseudoinverse which in turn defines the control ...generalized inverse and ...
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On the relation between Moore's and Penrose's conditions
... the existence and uniqueness of Λ were announced in [4], and proven in [5, pages 8, 202] after Moore’s death, where the reciprocal was renamed as the general reciprocal. However, the beauty of Moore’s definition was not ...
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Computing the Moore Penrose Inverse of a Matrix Through Symmetric Rank One Updates
... gorithm on each randomly generated matrix of various sizes. The recorded results coincide with the computa- tional complexity analysis perfectly. Observe that the performances of both algorithms are exactly the ...
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An explicit construction of fast cocyclic jacket transform on the finite field with any size
... φ (a, b)φ (a ◦ b, c) = φ (a, b ◦ c)φ (b, c), (1) where a, b, c ∈ G. A square matrix M(φ) whose row a and column b can be indexed by G with entry φ (a, b) ∈ C in position (a, b) under some fixed ordering, i.e., M(φ) ...
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Explicit inverse of the Pascal matrix plus one
... This paper presents a simple approach to invert the matrix Pn + In by applying the Euler polynomials and Bernoulli numbers, where Pn is the Pascal matrix.. Copyright © 2006 Hindawi Publi[r] ...
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Further Results on the Reverse Order Law for Inverse and Inverse of a Matrix Product
... Suppose that m − r A ≤ k − rB. Also note that r AB 1,3 I − AA † ≤ m − rA for arbitrary {1, 3}-inverses AB 1,3 . Therefore, for some AB 1,3 , 2.17 holds if and only if there is a {1, 3}-inverse AB 1,3 such that RAB ...
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Inverse Problems of Matrix Data Reconstruction
... We do have to point out two possible drawbacks of our algorithm. Firstly, it is hard to predict beforehand the depth of recursion needed for the calculation in the Sekitani and Yamamato algorithm. When p is large, the ...
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Computing Centre Newsletter No. 22, June 1978
... INVERSION OF MATRIX- POSITIVE DEFINITE- SYMMETRIC BAND MATRIX SYMMETRIC BAND STORAGE MODE SPACE ECONOMIZER SOLUTION.. PSEUDO INVERSE OF A MATRIX..[r] ...
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twistors and gauge fields
... According to the "twistor programme" of Penrose [4] relativistic fields are to be interpreted in terms of complex geometry of PT,.. under the Penrose correspondence?.[r] ...
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Title: Life Beyond Moore: More Moore or More than Moore – A Review
... by Moore‟s law, with two focused development arenas, namely, IC miniaturization down to nanodimension, and SoC based system ...keep Moore‟s law alive, there are ever-increasing awareness, R&D effort and ...
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A new method for the inverse of the square matrices
... study, inverse matrix finding method which is developed for the matrix of coefficients matrix in systems with n equations with n unknowns and used in the solution of linear equation systems is ...
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New inequalities for the Hadamard product of an M matrix and an inverse M matrix
... Some new convergent sequences of the lower bounds of the minimum eigenvalue τ B ◦ A–1 for the Hadamard product of B and A–1 are given.. Numerical examples are given to show that these s[r] ...
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