scholarly journals Quaternionic matrices: Unitary similarity, simultaneous triangularization and some trace identities

2008 ◽  
Vol 428 (4) ◽  
pp. 890-910 ◽  
Author(s):  
Dragomir Ž. Doković ◽  
Benjamin H. Smith
Keyword(s):  
Unitary Similarity ◽  
Simultaneous Triangularization

Simultaneous Triangularization of Algebras of Polynomially Compact Operators

1991 ◽  
Vol 34 (2) ◽  
pp. 260-264 ◽  
Author(s):  
M. Radjabalipour
Keyword(s):  
Hilbert Space ◽  
Jacobson Radical ◽  
Compact Operators ◽  
General Algebra ◽  
Closed Algebra ◽  
Quasinilpotent Operators ◽  
Simultaneous Triangularization

AbstractIf A is a norm closed algebra of compact operators on a Hilbert space and if its Jacobson radical J(A) consists of all quasinilpotent operators in A then A/ J(A) is commutative. The result is not valid for a general algebra of polynomially compact operators.

scholarly journals Preservers of unitary similarity functions on Lie products of matrices

2016 ◽  
Vol 498 ◽  
pp. 160-180 ◽  
Author(s):  
Jianlian Cui ◽  
Chi-Kwong Li ◽  
Yiu-Tung Poon
Keyword(s):  
Unitary Similarity ◽  
Similarity Functions ◽  
Products Of Matrices

On Simultaneous Triangularization of the Coefficients of Linear Systems

1996 ◽  
Author(s):  
W. C. Lee ◽  
F. Ma
Keyword(s):  
Linear Systems ◽  
Nonconservative System ◽  
Simultaneous Triangularization

Abstract The coefficients of a linear nonconservative system are arbitrary matrices lacking the usual properties of symmetry and definiteness. An efficient way for the analysis of a nonconservative system is to reduce its coefficient matrices simultaneously to upper triangular forms. The purpose of this paper is to present some criteria for simultaneous triangularization and, when applicable, to expound a constructive procedure for triangularization.

Preservers of radial unitary similarity functions on products of operators

2018 ◽  
Vol 542 ◽  
pp. 484-500 ◽  
Author(s):  
M. Bendaoud ◽  
A. Benyouness ◽  
M. Sarih ◽  
S. Sekkat
Keyword(s):  
Unitary Similarity ◽  
Similarity Functions

scholarly journals Unitary similarity to a normal matrix

2012 ◽  
Vol 436 (9) ◽  
pp. 3777-3783 ◽  
Author(s):  
Tatiana G. Gerasimova
Keyword(s):  
Normal Matrix ◽  
Unitary Similarity

scholarly journals Some Theorems On Matrices With Real Quaternion Elements

1955 ◽  
Vol 7 ◽  
pp. 191-201 ◽  
Author(s):  
N. A. Wiegmann
Keyword(s):  
Similarity Transformation ◽  
Elementary Divisor ◽  
Quaternion Matrix ◽  
Unitary Similarity ◽  
Triangular Form ◽  
Quaternion Matrices ◽  
Divisor Theory ◽  
Real Quaternion ◽  
Unitary Similarity Transformation

Matrices with real quaternion elements have been dealt with in earlier papers by Wolf (10) and Lee (4). In the former, an elementary divisor theory was developed for such matrices by using an isomorphism between n×n real quaternion matrices and 2n×2n matrices with complex elements. In the latter, further results were obtained (including, mainly, the transforming of a quaternion matrix into a triangular form under a unitary similarity transformation) by using a different isomorphism.

scholarly journals Unitary automorphisms of the space of Toeplitz-plus-Hankel matrices

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
A.K. Abdikalykov ◽  
V.N. Chugunov ◽  
Kh.D. Ikramov
Keyword(s):  
Toeplitz Matrices ◽  
Hankel Matrices ◽  
Unitary Matrices ◽  
Unitary Similarity

AbstractOur motivation was a paper of 1991 indicating three special unitary matrices that map Hermitian Toeplitz matrices by similarity into real Toeplitz-plus-Hankel matrices. Generalizing this result, we give a complete description of unitary similarity automorphisms of the space of Toeplitz-plus-Hankel matrices.

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