✦ LIBER ✦

A constructive decomposition and Fulkerson's characterization of permutation matrices

✍ Scribed by Patrick E. O'Neil

Publisher: Elsevier Science
Year: 1971
Tongue: English
Weight: 244 KB
Volume: 1
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(71)90026-4

No coin nor oath required. For personal study only.

✦ Synopsis

AbsOIcL Wc consider the se; of n x n ma,'rtces X = (x~i) fog which ~i~iEi~.,xii ~ ill ~-;3;-n, ft~r all t,J c: {I, 2 ..... n~. with x/j ;) 0 fo¢ all J, IE~i, 2, .... q}. it is sl~,;)wn that such ma-~:rk¢~ may bt (Ik ~:ompoted as X --$+ N. whe~.e S is a &~bly stochastic matrix 'and N is now ne~ttive in all entries. Th~ decomposition tech~ue is ,'(~sUuctive. This implies a result of Fttlketmn that t.~ rr~trices X, considerM as lyt,~g in R t~ form a convex polyhedron who~e wet'ti~s are the pennuta*,~on .ultllicer.. Finally, a sablet ~ 4[ the inequalities of ( I ) is sh~)wn to be "e~[", as as~ltcd by F~keman in I I I without i.roof..

📜 SIMILAR VOLUMES

A proof of Fulkerson's characterization

A proof of Fulkerson's characterization of permutation matrices

✍ Allan B. Cruse 📂 Article 📅 1975 🏛 Elsevier Science 🌐 English ⚖ 467 KB

A characterization of constructive dimen

A characterization of constructive dimension

✍ Satyadev Nandakumar 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 173 KB

## Abstract In the context of Kolmogorov's algorithmic approach to the foundations of probability, Martin‐Löf defined the concept of an individual random sequence using the concept of a constructive measure 1 set. Alternate characterizations use constructive martingales and measures of impossibilit

Incidence Matrices, Permutation Characte

Incidence Matrices, Permutation Characters, and the Minimal Genus of a Permutation Group

✍ Daniel Frohardt; Robert Guralnick; Kay Magaard 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 146 KB

Primitivity of Permutation Groups, Coher

Primitivity of Permutation Groups, Coherent Algebras and Matrices

✍ Gareth A. Jones; Mikhail Klin; Yossi Moshe 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 114 KB

A coherent algebra is F-primitive if each of its non-identity basis matrices is primitive in the sense of Frobenius. We investigate the relationship between the primitivity of a permutation group, the primitivity of its centralizer algebra, and F-primitivity. The results obtained are applied to give

A graph theoretical interpretation of no

A graph theoretical interpretation of nonsymmetric permutation on sparse matrices

✍ A. L. Sangiovanni-Vincentelli 📂 Article 📅 1977 🏛 John Wiley and Sons 🌐 English ⚖ 556 KB

## Abstract In the tableau approach to large‐electrical‐network analysis, as well as in structure analysis, the finite‐element method, linear programming etc., a very sparse linear algebraic set of equations **Ax = b** has to be solved repeatedly. To efficiently solve the system __via__ Gaussian el

Spectral Decomposition of Symmetric Oper

Spectral Decomposition of Symmetric Operator Matrices

✍ Reinhard Mennicken; Andrey A. Shkalikov 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 649 KB

The authors study symmetric operator matrices A B = ( B ' C ) in the product of Hilbert spaces H = Hi xH2, where the entries are not necessarily bounded operators. Under suitable assumptions the closure Lo exists and is a selfadjoint operator in H. With Lo, the closure of the transfer function M(X)