On a class of Jacobi-like procedures for diagonalising arbitrary real matrices

1979 ◽  
Vol 33 (2) ◽  
pp. 157-172 ◽  
Author(s):  
K. Veselić
Keyword(s):  
Real Matrices

scholarly journals Simplex algebras and their representation

1973 ◽  
Vol 14 (2) ◽  
pp. 136-144
Author(s):  
M. S. Vijayakumar
Keyword(s):  
Left Ideal ◽  
Maximal Ideal ◽  
Banach Algebras ◽  
Principal Component ◽  
Nonempty Interior ◽  
Regular Elements ◽  
Maximal Left Ideal ◽  
The Relationship ◽  
Order Identity ◽  
Real Matrices

This paper establishes a relationship (Theorem 4.1) between the approaches of A. C. Thompson [8, 9] and E. G. Effros [2] to the representation of simplex algebras, that is, real unital Banach algebras that are simplex spaces with the unit for order identity. It proves that the (nonempty) interior of the associated cone is contained in the principal component of the set of all regular elements of the algebra. It also conjectures that each maximal ideal (in the order sense—see below) of a simplex algebra contains a maximal left ideal of the algebra. This conjecture and other aspects of the relationship are illustrated by considering algebras of n × n real matrices.

Eigenvalues and Eigenvectors of Real Matrices

2009 ◽  
pp. 451-459
Author(s):  
Klaus Weltner ◽  
Peter Schuster ◽  
Wolfgang J. Weber ◽  
Jean Grosjean
Keyword(s):  
Eigenvalues And Eigenvectors ◽  
Real Matrices

Inverse problem for one-dimensional wave equation with matrix potential

2019 ◽  
Vol 27 (2) ◽  
pp. 217-223 ◽  
Author(s):  
Ammar Khanfer ◽  
Alexander Bukhgeim
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Uniqueness Theorem ◽  
Cauchy Data ◽  
Global Uniqueness ◽  
One Dimensional ◽  
Matrix Potential ◽  
The Matrix ◽  
Real Matrices ◽  
Dimensional Wave

AbstractWe prove a global uniqueness theorem of reconstruction of a matrix-potential {a(x,t)} of one-dimensional wave equation {\square u+au=0}, {x>0,t>0}, {\square=\partial_{t}^{2}-\partial_{x}^{2}} with zero Cauchy data for {t=0} and given Cauchy data for {x=0}, {u(0,t)=0}, {u_{x}(0,t)=g(t)}. Here {u,a,f}, and g are {n\times n} smooth real matrices, {\det(f(0))\neq 0}, and the matrix {\partial_{t}a} is known.

Rank, trace, eigenvalues and norms of a structured matrix

2019 ◽  
Vol 12 (06) ◽  
pp. 2040015
Author(s):  
Ahmet İpek
Keyword(s):  
Real Sequence ◽  
Simple Property ◽  
Structured Matrix ◽  
The Matrix ◽  
Matrix Formula ◽  
Appl Math ◽  
Real Matrices

The paper deals with rank, trace, eigenvalues and norms of the matrix [Formula: see text], where [Formula: see text] are ith components of any real sequence [Formula: see text]. A result in this paper is that the Euclidean and spectral norms of the matrix [Formula: see text] is [Formula: see text]. This is a generalization of the main result by Solak [Appl. Math. Comput. 232 (2014) 919–921], with the proof based on a simple property of norms of real matrices.

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