Outer inverses of matrices
نویسندگان
چکیده
منابع مشابه
Structured matrices and inverses
A matrix (and any associated linear system) will be referred to as structured if it has a small displacement rank. It is known that the inverse of a structured matrix is structured, which allows fast inversion (or solution), and reduced storage requirements. According to two definitions of displacement structure of practical interest, it is shown here that several types of inverses are also str...
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A new proof of the general representation for the entries of the inverse of any unreduced Hessenberg matrix of finite order is found. Also this formulation is extended to the inverses of reduced Hessenberg matrices. Those entries are given with proper Hessenbergians from the original matrix. It justifies both the use of linear recurrences for such computations and some elementary properties of ...
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Four results are given that address the existence, ambiguities and construction of a classical R-matrix given a Lax pair. They enable the uniform construction of R-matrices in terms of any generalized inverse of adL. For generic L a generalized inverse (and indeed the Moore-Penrose inverse) is explicitly constructed. The R-matrices are in general momentum dependent and dynamical. The constructi...
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Bounds for the ranks of upper-right submatrices of a generalized inverse of a strictly lower k-banded matrix are obtained. It is shown that such ranks can be exactly predicted under some conditions. The proof uses the Nullity Theorem and bordering technique for generalized inverse.
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AproductADF1 : : : FN of invertible block-diagonalmatrices will be bandedwith a banded inverse. We establish this factorization with the numberN controlled by the bandwidthsw and not by the matrix size n:When A is an orthogonal matrix, or a permutation, or banded plus finite rank, the factors Fi have w D 1 and generate that corresponding group. In the case of infinite matrices, conjectures rema...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2002
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(01)00583-3