Titlebook: Combinatorial Matrix Theory and Generalized Inverses of Matrices; Ravindra B. Bapat,Steve J. Kirkland,Simo Puntanen Book 2013 Springer Ind

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maladorit

獨(dú)白

Products and Sums of Idempotent Matrices over Principal Ideal Domains,of writing a square matrix as a sum of idempotent matrices. Much work was done for real matrices and for matrices over other algebraic structures. We shall consider some of this work and present some new results for matrices over projective free rings.

Mere僅僅

Perfect Semiring of Nonnegative Matrices,r right perfect if and only if it is closed under Drazin inverse of all elements. Furthermore, each nonnil right and left ideal contains a nonzero idempotent. This generalizes the known result on the characterization of finite semigroups of nonnegative matrices.

cortex

Regular Matrices over an Incline,We discuss the regularity of matrices over .. We obtain equivalent conditions for the existence of various generalized inverses of an incline matrix. We provide an algorithm for the regularity of matrices over . and illustrate with suitable examples.

VOC

Matrix Partial Orders Associated with Space Preorder,gular matrices. Particularly, we consider partial order defined by space decomposition, star ordering, and minus partial order for our discussion. These relations are closely associated with comparison of column spaces and row spaces of matrices. Results associated with selected matrix relation that

Confirm

售穴

Haruo Sugi,Shigeru Chaen,Ibuki Shirakawa energy of the underlying hypercube, distinct from the two orientations of hypercubes defined by Tian (Linear Algebra Appl. 435:2140–2149, .) and show how one of the two orientations of .. described by Tian is a special case of our method.

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Modern Experimental Methods and Results,he method of moments is used. To transform mixed third-order moments into a parameter vector, the star product of matrices is used; for star product and its applications, see, for example, Kollo (J.?Multivar. Anal. 99:2328–2338, .) or Visk (Commun. Stat. 38:461–470, .). Results of the first applications are shortly described and referred to.

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