Eventual properties of matrices
نویسندگان
چکیده
An eventual property of a matrix M ∈ C is a property that holds for all powers M, k ≥ k0, for some positive integer k0. Eventually positive and eventually nonnegative matrices have been studied extensively, and some results are known for eventually r-cyclic matrices. This paper introduces and establishs properties of eventually reducible matrices, establishs properties of the eigenstructure of eventually r-cyclic matrices, and answers affirmatively a question of Zaslavsky and Tam about eventually nonnegative matrices.
منابع مشابه
Ela Eventual Properties of Matrices
Abstract. An eventual property of a matrix M ∈ C is a property that holds for all powers M, k ≥ k0, for some positive integer k0. Eventually positive and eventually nonnegative matrices have been studied extensively, and some results are known for eventually r-cyclic matrices. This paper introduces and establishs properties of eventually reducible matrices, establishs properties of the eigenstr...
متن کاملEventual Properties of Matrices ∗ Leslie Hogben
An eventual property of a matrix M ∈ C n×n is a property that holds for all powers M k , k ≥ k 0 , for some positive integer k 0. Eventually positive and eventually nonnegative matrices have been studied extensively, and some results are known for eventually r-cyclic matrices. In this paper we introduce and establish properties of eventually reducible matrices, establish properties of the eigen...
متن کاملProperties of Central Symmetric X-Form Matrices
In this paper we introduce a special form of symmetric matrices that is called central symmetric $X$-form matrix and study some properties, the inverse eigenvalue problem and inverse singular value problem for these matrices.
متن کاملEffect of Particle Size, Compaction Force and Presence of Aerosil 200 on the Properties of Matrices Prepared from Physical Mixture of Propranolol Hydrochloride and Eudragit RS or RL
Objective Eudragits are widely used polymers in the production of oral sustained release dosage forms. The application of these polymers in the production of inert insoluble matrices has been investigated. However the effect of particle size, compaction force and presence of Aerosil 200 as a glidant on the properties of Eudragit RS and RL matrices prepared by direct compression of their physic...
متن کاملProperties of matrices with numerical ranges in a sector
Let $(A)$ be a complex $(ntimes n)$ matrix and assume that the numerical range of $(A)$ lies in the set of a sector of half angle $(alpha)$ denoted by $(S_{alpha})$. We prove the numerical ranges of the conjugate, inverse and Schur complement of any order of $(A)$ are in the same $(S_{alpha})$.The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product, star-congruen...
متن کامل