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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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Generalized Inverse of a Finite Graph
Fundamenta Informaticae, 1981We define the optimal generalized inverse of the directed graph, give its construction and prove that the graph has an inverse graph iff its optimal generalized inverse is its inverse. The construction of the optimal generalized inverse may be used in the preparation of the PERT networks by the computer.
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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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Dual core generalized inverse of third-order dual tensor based on the T-product
Computational and Applied Mathematics, 2022Haifeng Ma, Ma Haifeng
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On a new generalized inverse for Hilbert space operators
Quaestiones Mathematicae, 2020Jianlong Chen +2 more
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On integral representation of the generalized inverse AT,S(2)
Applied Mathematics and Computation, 2003Yimin Wei, Dragan S Djordjevic
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Full-rank representation of generalized inverse AT,S(2) and its application
Computers and Mathematics With Applications, 2007Xingping Sheng
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On Generalized Inverses of Matrices
SIAM Journal on Applied Mathematics, 1967openaire +2 more sources