Results 231 to 240 of about 691,972 (277)
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1990
Abstract Consider again the set of linear equations in n unknowns. We saw in Chapter 4 that when A is n × n and has a non-zero determinant, then the unique solution of (10.1) is x = Aȃ1 b, where Aȃ1 is the inverse of A. However, in Chapter 5 we studied the important problem of solving (10.1) when A is singular or rectangular.
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Abstract Consider again the set of linear equations in n unknowns. We saw in Chapter 4 that when A is n × n and has a non-zero determinant, then the unique solution of (10.1) is x = Aȃ1 b, where Aȃ1 is the inverse of A. However, in Chapter 5 we studied the important problem of solving (10.1) when A is singular or rectangular.
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Generalized inverses inC*-Algebras
Rendiconti del Circolo Matematico di Palermo, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The generalized inverse and inverse structure
Acta Crystallographica Section A, 1977When a structure in one space is projected or mapped or otherwise described in another space or 'language', then the transformation is usually irreversible. In the case of linear transformations a generalized inverse matrix exists even if the transformation matrix is rectangular or singular.
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Archive for Rational Mechanics and Analysis, 1976
The existence of the Moore-Penrose inverse is discussed for elements of a *-regular ring \(R\). A technique is developed for computing conditional and reflexive inverses for matrices in \(R_{2\times 2}\), which is then used to calculate the Moore-Penrose inverse for these matrices.
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The existence of the Moore-Penrose inverse is discussed for elements of a *-regular ring \(R\). A technique is developed for computing conditional and reflexive inverses for matrices in \(R_{2\times 2}\), which is then used to calculate the Moore-Penrose inverse for these matrices.
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2001
The Fourier inversion formula is a standard fact of elementary analysis. Harish-Chandra developed an inversion for K-bi-invariant functions on a semisimple Lie group G, in other words he developed the theory of a spherical transform [Har 58a], [Har 58b], which is an integral transform, with a kernel called the spherical kernel.
Jay Jorgenson, Serge Lang
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The Fourier inversion formula is a standard fact of elementary analysis. Harish-Chandra developed an inversion for K-bi-invariant functions on a semisimple Lie group G, in other words he developed the theory of a spherical transform [Har 58a], [Har 58b], which is an integral transform, with a kernel called the spherical kernel.
Jay Jorgenson, Serge Lang
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Generalized inverses and generalized splines
Numerical Functional Analysis and Optimization, 1980An abstract framework in Hilbert space is provided for generalized splines and generalized inverses of operators.
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2011
Let A be a square matrix of order n. If it is nonsingular, then Ker(A) = {0} and, as mentioned earlier, the solution vector x in the equation y = Ax is determined uniquely as x = A -1 y. Here, A -1 is called the inverse (matrix) of A defining the inverse transformation from y ∈ En to x ∈ Em, whereas the matrix A represents a transformation from x to y.
Haruo Yanai, Kei Takeuchi, Yoshio Takane
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Let A be a square matrix of order n. If it is nonsingular, then Ker(A) = {0} and, as mentioned earlier, the solution vector x in the equation y = Ax is determined uniquely as x = A -1 y. Here, A -1 is called the inverse (matrix) of A defining the inverse transformation from y ∈ En to x ∈ Em, whereas the matrix A represents a transformation from x to y.
Haruo Yanai, Kei Takeuchi, Yoshio Takane
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On a new generalized inverse for Hilbert space operators
Quaestiones Mathematicae, 2020Jianlong Chen +2 more
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