A new notion of coneigenvalue was introduced by Ikramov in [On pseudo-eigenvalues and singular numbers of a complex square matrix, (in Russian), Zap. Nauchn. Semin. POMI 334 (2006), 111-120]. This paper presents some majorization inequalities for coneigenvalues, which extend some classical majorization relations for eigenvalues and singular values, and may serve as a basis for further investiga...

We propose two numerical methods, namely the block relaxation and majorization method, for the problem of nearest correlation matrix with factor structure, which is highly nonconvex. In the block relaxation method, the subproblem is of the standard trust region problem, which is solved by Steighaug’s truncated conjugate gradient method or by the trust region method of [21]. In the majorization ...

Let Mn,m be the set of all n × m matrices with entries in F, where F is the field of real or complex numbers. A matrix R ∈ Mn with the property Re=e, is said to be a g-row stochastic (generalized row stochastic) matrix. Let A,B∈ Mn,m, so B is said to be gw-majorized by A if there exists an n×n g-row stochastic matrix R such that B=RA. In this paper we characterize all linear operators that stro...

in this paper we study the concept of latin-majorizati-on. geometrically this concept is different from other kinds of majorization in some aspects. since the set of all $x$s latin-majorized by a fixed $y$ is not convex, but, consists of :union: of finitely many convex sets. next, we hint to linear preservers of latin-majorization on $ mathbb{r}^{n}$ and ${m_{n,m}}$.

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We explore the combinatorial properties of a particular type of extension monoid product of preinjective Kronecker modules. The considered extension monoid product plays an important role in matrix completion problems. We state theorems which characterize this product in both implicit and explicit ways and we prove that the conditions given in the definition of the generalized majorization are ...

In this paper, we give the factorizations of Lucas and inverse matrices. We also investigate Cholesky factorization symmetric matrix. Moreover, obtain upper lower bounds for eigenvalues matrix by using some majorization techniques.