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 ...

We introduce the concept of weak k-majorization extending the classical notion of weak sub-majorization. For integers k and n with k n a vector x 2 R is weakly k-majorized by a vector q 2 R if the sum of the r largest components of x does not exceed the sum of the r largest components of q, for r = 1; : : : ; k. For a given q the set of vectors weakly k-majorized by q de nes a polyhedron P (q;k...

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.

Given a linear map T on Euclidean Jordan algebra of rank n, we consider the set all nonnegative vectors q in Rn with decreasing components that satisfy pointwise weak-majorization inequality λ(|T(x)|)≺w⁡q∗λ(|x|), where λ is eigenvalue and ∗ denotes componentwise product Rn. With respect to ordering, show existence least vector this set. When positive map, shown be join (in order) T(e) T∗(e), e ...