摘要:

LetRbe a finite dimensional central simple algebra over a fieldFAbe anyn×nmatrix overR. By using the method of matrix representation, this paper obtains the structure formula of the minimal polynomialqA(λ) ofAoverF. By usingqA(λ), this paper discusses the structure of right (left) eigenvalues set ofA, and obtains the necessary and sufficient condition that a matrix over a finite dimensional central division algebra is similar to a diagonal matrix.

ISSN:0308-1087    

DOI:10.1080/03081089808818580

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

LetTbe a completely nonunitary contraction with rank (l−T*T)=l on an n-dimensional Hilbert space. We prove that (1) ifn= 2 andSis an operator which has norm 1, attains its norm and satisfiesW(S) ⊆W(T), thenShasTas a direct summand, and (2) ifn≥ 3 andSis an operator such thatSkdilates tosimultaneously fork=l,2,…,n−1 andthenShasTas a direct summand. (HereW(·) denotes the numerical range). These results generalize the corresponding ones forTthen×nnilpotent Jordan block.

ISSN:0308-1087    

DOI:10.1080/03081089808818581

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

In this study, we have found an upper and lower bounds for thenorm (1 <p<∞) of Cauchy-Toeplitz matrix in the formTn=Moreover, we have given a conjecture for thenorm of this matrix.

ISSN:0308-1087    

DOI:10.1080/03081089808818582

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

The Drazin inverse of a 2×2 block matrixis considered. Expressions for

ISSN:0308-1087    

DOI:10.1080/03081089808818583

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

An elementary and direct proof of the Szegö formula is given, for both eigen and singular values. This proof, which is based on tools from linear algebra and does not rely on the theory of Fourier series, simultaneously embraces multilevel Toeplitz matrices, block Toeplitz matrices and combinations of them. The assumptions on the generating

ISSN:0308-1087    

DOI:10.1080/03081089808818584

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

LetLbe the Laplacian matrix of a tree. We present a graph-theoretic interpretation of the cofactors of order 2 ofL. From this, we deduce a description for the inverse of the rooted Laplacian, reflecting the geometry of a branch. Defining the thickness of a branch as the Perron root of this matrix, we present a minimax-characterization of the characteristic center of the tree based on the thickness of its branches.

ISSN:0308-1087    

DOI:10.1080/03081089808818585

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

We consider linear preserver problems on the algebra of upper triangular matrices. We obtain the general form of nonsingular linear maps preserving rank one idempotents or commutativity. We give examples to show that the nonsingularity assumption is essential in our results.

ISSN:0308-1087    

DOI:10.1080/03081089808818586

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

In this work we deal with group involutory matrices, i.e.A#=A. We give necessary and sufficient conditions to characterize these matrices in terms of different representations of the group inverse. First, we give different expressions of the group inverse of a square matrixA. In addition, the special case of integer matrices is considered.

ISSN:0308-1087    

DOI:10.1080/03081089808818587

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

We prove that Radon transforms associated to directed graphs determine a representation of the ring of isomorphism classes of directed graphs sharing a fixed setXof vertices in the complex vector space. We also express Laplacians in terms of Radon transforms, determine the Laplacians associated to the sum and product of directed graphs, and describe a relation between Laplacians and flows in directed graphs.

ISSN:0308-1087    

DOI:10.1080/03081089808818588

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

We determine the invertibilty or singularity, as appropriate, for all (positive) integral Hadamard powers of distance matrices.

ISSN:0308-1087    

DOI:10.1080/03081089808818589

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor