COMPUTATIONS FOR ALGEBRAS AND GROUP
... This thesis is an examination of several problems which arise in the structure theory of associative algebras and matrix representations of groups, from the standpoint of computational complexity. We begin with computational problems corresponding to the Wedderburn decomposition of matrix algebras o ...
... This thesis is an examination of several problems which arise in the structure theory of associative algebras and matrix representations of groups, from the standpoint of computational complexity. We begin with computational problems corresponding to the Wedderburn decomposition of matrix algebras o ...
Introduction to Group Theory
... Given two groups G1 = {ai } and G2 = {bk }, their outer direct product is the group G1 × G2 with elements (ai , bk ) and multiplication (ai , bk ) · (aj , bl ) = (ai aj , bk bl ) ∈ G1 × G2 • Check that the group axioms are satisfied for G1 × G2 . • Order of Gn is hn (n = 1, 2) ⇒ order of G1 × G2 is ...
... Given two groups G1 = {ai } and G2 = {bk }, their outer direct product is the group G1 × G2 with elements (ai , bk ) and multiplication (ai , bk ) · (aj , bl ) = (ai aj , bk bl ) ∈ G1 × G2 • Check that the group axioms are satisfied for G1 × G2 . • Order of Gn is hn (n = 1, 2) ⇒ order of G1 × G2 is ...
- Wyoming Scholars Repository
... [10] B.-L. Yu and T.-Z. Huang. On minimal potentially power-positive sign patterns. Operators and Matrices, 6:159–167, 2012. [11] B.-L. Yu, T.-Z. Huang, C. Hong, and D.D. Wang. Eventual positivity of tridiagonal sign patterns. Linear and Multilinear Algebra, 62:853–85 ...
... [10] B.-L. Yu and T.-Z. Huang. On minimal potentially power-positive sign patterns. Operators and Matrices, 6:159–167, 2012. [11] B.-L. Yu, T.-Z. Huang, C. Hong, and D.D. Wang. Eventual positivity of tridiagonal sign patterns. Linear and Multilinear Algebra, 62:853–85 ...
Limiting Laws of Coherence of Random Matrices with Applications
... To be more specific, suppose we observe independent and identically distributed pvariate random variables Y1 , . . . , Yn with mean µ = µp×1 , covariance matrix Σ = Σp×p and correlation matrix R = Rp×p . In the setting where the dimension p and the sample size n are comparable, i.e., n/p → γ ∈ (0, ...
... To be more specific, suppose we observe independent and identically distributed pvariate random variables Y1 , . . . , Yn with mean µ = µp×1 , covariance matrix Σ = Σp×p and correlation matrix R = Rp×p . In the setting where the dimension p and the sample size n are comparable, i.e., n/p → γ ∈ (0, ...
Chapter 2 The simplex method - EHU-OCW
... two or three variables. In Chapter 1 the graphical solution of two variable linear models has been analyzed. It is not possible to solve linear models of more than three variables by using the graphical solution, and therefore, it is necessary to use an algebraic procedure. In 1949, George B. Dantzi ...
... two or three variables. In Chapter 1 the graphical solution of two variable linear models has been analyzed. It is not possible to solve linear models of more than three variables by using the graphical solution, and therefore, it is necessary to use an algebraic procedure. In 1949, George B. Dantzi ...
1: Introduction to Lattices
... distance at least kx − yk ≥ . Not every subgroup of Rn is a lattice. Example 1. Qn is a subgroup of Rn , but not a lattice, because it is not discrete. The simplest example of lattice is the set of all n-dimensional vectors with integer entries. Example 2. The set Zn is a lattice because integer ve ...
... distance at least kx − yk ≥ . Not every subgroup of Rn is a lattice. Example 1. Qn is a subgroup of Rn , but not a lattice, because it is not discrete. The simplest example of lattice is the set of all n-dimensional vectors with integer entries. Example 2. The set Zn is a lattice because integer ve ...