Generalized inverses of substochastic matrices
نویسندگان
چکیده
منابع مشابه
R-Matrices and Generalized Inverses
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.
متن کاملSpecial forms of generalized inverses of row block matrices
Given a row block matrix [A, B ], this paper investigates the relations between the generalized inverse [A, B ]− and the column block matrix [ A− B− ] consisting of two generalized inverses A− and B−. The first step of the investigation is to establish a formula for the minimal rank of the difference [A, B ]− − [ A− B− ] , the second step is to find a necessary and sufficient condition for [A, ...
متن کاملOn Algebraic Properties of Generalized Inverses of Matrices
In this paper, we will study algebraic properties of the generalized inverses of the sum and the product of two matrices. By using rank additivity we explicit the generalized inverse of the sum of two matrices if their range spaces are not disjoint and we give a numerical example in this case. We will also use projectors to express the general form of a generalized inverse of the product of two...
متن کاملForms of Generalized Inverses of Row Block Matrices
Given a row block matrix [A, B ], this paper investigates the relations between the generalized inverse [A, B ]− and the column block matrix [ A− B− ] consisting of two generalized inverses A− and B−. The first step of the investigation is to establish a formula for the minimal rank of the difference [A, B ]− − [ A− B− ] , the second step is to find a necessary and sufficient condition for [A, ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1987
ISSN: 0024-3795
DOI: 10.1016/0024-3795(87)90063-2