scholarly journals A decomposition of the tensor product of matrices

Filomat ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 105-124
Author(s):  
Caixing Gu ◽  
Jaehui Park
Keyword(s):  
Tensor Product ◽  
Unitary Equivalence ◽  
Direct Sum ◽  
Product Of Matrices

In this paper we decompose (under unitary equivalence) the tensor product A ? A into a direct sum of irreducible matrices, when A is a 3 x 3 matrix.

scholarly journals Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Arnon Ploymukda ◽  
Pattrawut Chansangiam
Keyword(s):  
Tensor Product ◽  
Hilbert Spaces ◽  
Hadamard Product ◽  
Operator Matrices ◽  
Linear Map ◽  
Direct Sum ◽  
Positive Linear Map ◽  
Algebraic Properties ◽  
Product Of Matrices

We introduce the notion of Khatri-Rao product for operator matrices acting on the direct sum of Hilbert spaces. This notion generalizes the tensor product and Hadamard product of operators and the Khatri-Rao product of matrices. We investigate algebraic properties, positivity, and monotonicity of the Khatri-Rao product. Moreover, there is a unital positive linear map taking Tracy-Singh products to Khatri-Rao products via an isometry.

Algebraic method of simplifying Boolean networks using semi‐tensor product of Matrices

2019 ◽  
Vol 21 (6) ◽  
pp. 2569-2577 ◽  
Author(s):  
Yongyi Yan ◽  
Jumei Yue ◽  
Zengqiang Chen
Keyword(s):  
Tensor Product ◽  
Algebraic Method ◽  
Boolean Networks ◽  
Product Of Matrices

scholarly journals On Modular Representation Algebras and a Class of Matrix Algebras

1982 ◽  
Vol 33 (3) ◽  
pp. 351-355 ◽  
Author(s):  
J-C. Renaud
Keyword(s):  
Tensor Product ◽  
Cyclic Group ◽  
Prime Order ◽  
Matrix Algebra ◽  
Modular Representation ◽  
Complex Field ◽  
Matrix Algebras ◽  
Direct Sum ◽  
Standard Operations

AbstractLet G be a cyclic group of prime order p and K a field of characteristic p. The set of classes of isomorphic indecomposable (K, G)-modules forms a basis over the complex field for an algebra p (Green, 1962) with addition and multiplication being derived from direct sum and tensor product operations.Algebras n with similar properties can be defined for all n ≥ 2. Each such algebra is isomorphic to a matrix algebra Mn of n × n matrices with complex entries and standard operations. The characters of elements of n are the eigenvalues of the corresponding matrices in Mn.

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