Displaying similar documents to “On the matrix form of Kronecker lemma”

Intervals of certain classes of Z-matrices

M. Rajesh Kannan, K.C. Sivakumar (2014)

Discussiones Mathematicae - General Algebra and Applications

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Let A and B be M-matrices satisfying A ≤ B and J = [A,B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible M-matrix and A ≤ B, then aA + bB is an invertible M-matrix for all a,b > 0. In this article, we present an elementary proof of a stronger version of this result and study corresponding results for certain other classes as well.

A note on the matrix Haffian.

Heinz Neudecker (2000)

Qüestiió

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This note contains a transparent presentation of the matrix Haffian. A basic theorem links this matrix and the differential ofthe matrix function under investigation, viz ∇F(X) and dF(X). Frequent use is being made of matrix derivatives as developed by Magnus and Neudecker.

Sufficient conditions to be exceptional

Charles R. Johnson, Robert B. Reams (2016)

Special Matrices

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A copositive matrix A is said to be exceptional if it is not the sum of a positive semidefinite matrix and a nonnegative matrix. We show that with certain assumptions on A−1, especially on the diagonal entries, we can guarantee that a copositive matrix A is exceptional. We also show that the only 5-by-5 exceptional matrix with a hollow nonnegative inverse is the Horn matrix (up to positive diagonal congruence and permutation similarity).

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.