Displaying similar documents to “A theorem on polygons in n dimensions with applications to variation-diminishing and cyclic variation-diminishing linear transformations”

Indecomposable (1,3)-groups and a matrix problem

David M. Arnold, Adolf Mader, Otto Mutzbauer, Ebru Solak (2013)

Czechoslovak Mathematical Journal

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Almost completely decomposable groups with a critical typeset of type ( 1 , 3 ) and a p -primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient p k , either no indecomposables if k ≤ 2 ; only six near isomorphism types of indecomposables if k = 3 ; and indecomposables of arbitrary large rank if k ≥ 4 .

Possible numbers ofx’s in an {x,y}-matrix with a given rank

Chao Ma (2017)

Open Mathematics

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Let x, y be two distinct real numbers. An {x, y}-matrix is a matrix whose entries are either x or y. We determine the possible numbers of x’s in an {x, y}-matrix with a given rank. Our proof is constructive.

On a nonnegative irreducible matrix that is similar to a positive matrix

Raphael Loewy (2012)

Open Mathematics

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Let A be an n×n irreducible nonnegative (elementwise) matrix. Borobia and Moro raised the following question: Suppose that every diagonal of A contains a positive entry. Is A similar to a positive matrix? We give an affirmative answer in the case n = 4.

Basic Properties of the Rank of Matrices over a Field

Karol Pąk (2007)

Formalized Mathematics

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In this paper I present selected properties of triangular matrices and basic properties of the rank of matrices over a field.I define a submatrix as a matrix formed by selecting certain rows and columns from a bigger matrix. That is in my considerations, as an array, it is cut down to those entries constrained by row and column. Then I introduce the concept of the rank of a m x n matrix A by the condition: A has the rank r if and only if, there is a r x r submatrix of A with a non-zero...