ON A CERTAIN METHOD FOR DETERMINING THE NON-SINGULARITY OF AN INTEGRAL MATRIX

2018 ◽  
Vol 104 (2) ◽  
pp. 221-227
Author(s):  
F. Maruyama ◽  
Y. Deguchi ◽  
M. Toyoizumi
Keyword(s):  
Integral Matrix

scholarly journals The graded Cartan matrix and global dimension of 0-relations algebras

1987 ◽  
Vol 30 (3) ◽  
pp. 351-362 ◽  
Author(s):  
W. D. Burgess
Keyword(s):  
Artinian Ring ◽  
Global Dimension ◽  
Cartan Matrix ◽  
Integral Matrix ◽  
Finite Global Dimension ◽  
Composition Factors

The Cartan matrix C of a left artinian ring A, with indecomposable projectives P1,…,Pn and corresponding simples Si=Pi/JPi, is an n×n integral matrix with entries Cij, the number of copies of the simple sj which appear as composition factors of Pi. A relationship between the invertibility of this matrix (as an integral matrix) and the finiteness of the global dimension has long been known: gl dim A < ∞⇒det C = ± 1 (Eilenberg [3]). More recently Zacharia [9] has shown that gl dim A ≦ 2⇒det C = 1, and in fact no rings of finite global dimension are known with det C = −1. The converse, det C = l⇒gl dim A < ∞, is false, as easy examples show ([[1) or [3]). However if A is left serial, gl dim A < ∞iff det C = l [1]. If A = ⊕n ≧ 0 An is ℤ-graded and the radical J = ⊕n ≧ 0 An, Wilson [8] calls such rings positively graded. Here there is a graded Cartan matrix with entries from ℤ[X] and gl dim A < ∞⇒det = 1 and, hence, det C = l [8, Prop. 2.2].

scholarly journals On the orbit-stabilizer problem for integral matrix actions of polycyclic groups

2003 ◽  
Vol 72 (243) ◽  
pp. 1511-1530 ◽  
Author(s):  
Bettina Eick ◽  
Gretchen Ostheimer
Keyword(s):  
Integral Matrix ◽  
Polycyclic Groups

scholarly journals Surjectivity of near-square random matrices

2019 ◽  
Vol 29 (2) ◽  
pp. 267-292
Author(s):  
Hoi. H. Nguyen ◽  
Elliot Paquette
Keyword(s):  
Random Matrices ◽  
High Probability ◽  
Sparse Matrices ◽  
Integral Lattice ◽  
Integral Matrix ◽  
Random Integral ◽  
Very High ◽  
Dependent Entries ◽  
Independent And Identically Distributed

AbstractWe show that a nearly square independent and identically distributed random integral matrix is surjective over the integral lattice with very high probability. This answers a question by Koplewitz [6]. Our result extends to sparse matrices as well as to matrices of dependent entries.

An integral matrix-based technique for systematic systolic design

Integration ◽  
1996 ◽  
Vol 20 (3) ◽  
pp. 269-285 ◽  
Author(s):  
F Lorenzelli ◽  
K Yao
Keyword(s):  
Integral Matrix

Assessment of Real Gas Effects on Approximate and Boundary Layer Equations for Hypersonic Laminar Flow over Axisymmetric Bodies

2014 ◽  
Vol 1016 ◽  
pp. 534-539
Author(s):  
Ramin Kamali Moghadam ◽  
Seyed Amir Hosseini
Keyword(s):  
Boundary Layer ◽  
Body Region ◽  
Integral Matrix ◽  
Real Gas ◽  
Boundary Layer Equations ◽  
Blunt Bodies ◽  
Real Gas Effects ◽  
Efficient Code ◽  
Computational Procedures ◽  
Axisymmetric Bodies

Two efficient computational procedures based on the boundary layer equations and approximate relations areassessedin prediction of the laminar hypersonic flowfield for both the perfect gas and equilibrium air around the axisymmetric blunt body configurations. For the boundary layer procedure, the boundary layer equationsutilize the integral matrix solution algorithm for the blunt nose and after body region by using a space marching technique. The integral matrix procedure able us to create accurate and smooth results using the minimum grid in the boundary layer and minimize the computational costs. Applying the approximate method creates a robust and efficient code for heating calculations over the blunt bodies which flies in hypersonic regimes. These algorithms are highly appropriate to design of hypersonic reentry vehicles. The effects of real gas on the flowfield characteristics are also studied in two procedures.

Sign in / Sign up

Export Citation Format

Share Document