The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “A basic decomposition result related to the notion of the rank of a matrix and applications.”

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

Chao Ma (2017)

Open Mathematics

Similarity:

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 the Yang-Baxter-like matrix equation for rank-two matrices

Duanmei Zhou, Guoliang Chen, Jiu Ding (2017)

Open Mathematics

Similarity:

Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX. Together with a previous paper devoted to the case that QTP is nonsingular, we have completely solved the matrix equation with any given matrix A of rank-two.

Remarks on the Sherman-Morrison-Woodbury formulae

Miroslav Fiedler (2003)

Mathematica Bohemica

Similarity:

We present some results on generalized inverses and their application to generalizations of the Sherman-Morrison-Woodbury-type formulae.

Zero-term rank preservers of integer matrices

Seok-Zun Song, Young-Bae Jun (2006)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

The zero-term rank of a matrix is the minimum number of lines (row or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve the zero-term rank of the m × n integer matrices. That is, a linear operator T preserves the zero-term rank if and only if it has the form T(A)=P(A ∘ B)Q, where P, Q are permutation matrices and A ∘ B is the Schur product with B whose entries are all nonzero integers.

A bound for the rank-one transient of inhomogeneous matrix products in special case

Arthur Kennedy-Cochran-Patrick, Sergeĭ Sergeev, Štefan Berežný (2019)

Kybernetika

Similarity:

We consider inhomogeneous matrix products over max-plus algebra, where the matrices in the product satisfy certain assumptions under which the matrix products of sufficient length are rank-one, as it was shown in [6] (Shue, Anderson, Dey 1998). We establish a bound on the transient after which any product of matrices whose length exceeds that bound becomes rank-one.

From geometry to invertibility preservers

Hans Havlicek, Peter Šemrl (2006)

Studia Mathematica

Similarity:

We characterize bijections on matrix spaces (operator algebras) preserving full rank (invertibility) of differences of matrix (operator) pairs in both directions.