Power Indices of Trace Zero Symmetric Boolean Matrices
نویسندگان
چکیده
The power index of a square Boolean matrix A is the least integer d such that A is a linear combination of previous nonnegative powers of A. We determine the maximum power indices for the class of n × n primitive symmetric Boolean matrices of trace zero, the class of n × n irreducible nonprimitive symmetric Boolean matrices, and the class of n×n reducible symmetric Boolean matrices of trace zero, and characterize the extreme matrices respectively.
منابع مشابه
Sets of Weak Exponents of Indecomposability for Irreducible Boolean Matrices
Let IBn be the set of all irreducible matrices in Bn and let SIBn be the set of all symmetric matrices in IBn. Finding an upper bound for the set of indices of matrices in IBn and SIBn and determining gaps in the set of indices of matrices in IBn and SIBn has been studied by many researchers. In this paper, we establish a best upper bound for the set of weak exponents of indecomposability of ma...
متن کاملTRIANGULAR FUZZY MATRICES
In this paper, some elementary operations on triangular fuzzynumbers (TFNs) are defined. We also define some operations on triangularfuzzy matrices (TFMs) such as trace and triangular fuzzy determinant(TFD). Using elementary operations, some important properties of TFMs arepresented. The concept of adjoints on TFM is discussed and some of theirproperties are. Some special types of TFMs (e.g. pu...
متن کاملEla Constructions of Trace Zero Symmetric Stochastic Matrices for the Inverse Eigenvalue Problem∗
In the special case of where the spectrum σ = {λ1, λ2, λ3, 0, 0, . . . , 0} has at most three nonzero eigenvalues λ1, λ2, λ3 with λ1 ≥ 0 ≥ λ2 ≥ λ3, and λ1 + λ2 + λ3 = 0, the inverse eigenvalue problem for symmetric stochastic n × n matrices is solved. Constructions are provided for the appropriate matrices where they are readily available. It is shown that when n is odd it is not possible to re...
متن کاملBuckling Behaviors of Symmetric and Antisymmetric Functionally Graded Beams
The present study investigates buckling characteristics of both nonlinear symmetric power and sigmoid functionally graded (FG) beams. The volume fractions of metal and ceramic are assumed to be distributed through a beam thickness by the sigmoid-law distribution (S-FGM), and the symmetric power function (SP-FGM). These functions have smooth variation of properties across the boundary rather tha...
متن کاملReliability assessment of power distribution systems using disjoint path-set algorithm
Finding the reliability expression of different substation configurations can help design a distribution system with the best overall reliability. This paper presents a computerized a nd implemented algorithm, based on Disjoint Sum of Product (DSOP) algorithm. The algorithm was synthesized and applied for the first time to the determination of reliability expression of a substation to determine...
متن کامل