The c-spectralc-radial and c-convex matrices
- 1 November 1986
- journal article
- research article
- Published by Taylor & Francis in Linear and Multilinear Algebra
- Vol. 20 (1) , 5-15
- https://doi.org/10.1080/03081088608817739
Abstract
Let c=(c 1,…cn ) be a complex row vector and [c] be the diagonal matrix with c 1,…cn as its diagonal entries. Given an n×n complex matrix A with eigenvalues α j , 1≦j≦n, we define as the c-eigenpolygonc-numerical rangec-spectral radiusc-numerical radius and c-spectral norm of A respectively. For c = (1,0,…, 0) they are reduced to the classical eigenpolygon, numerical range, spectral radius, numerical radius and spectral norm of A. We say that the matrix A is c-spectral if pc (A) =rc (A)c-radial if pc (A) = ||A|| c , and c-convex if Pc (A) = Wc (A). In this note we give characterizations of these matrices and study their properties.Keywords
This publication has 9 references indexed in Scilit:
- The generalized spectral radius, numerical radius and spectral normLinear and Multilinear Algebra, 1984
- A conjecture of marcus on the generalized numerical rangeLinear and Multilinear Algebra, 1983
- SOME COMBINATORIAL ASPECTS OF NUMERICAL RANGE*Annals of the New York Academy of Sciences, 1979
- On certain finite dimensional numerical ranges and numerical radii†Linear and Multilinear Algebra, 1979
- Nondifferentiable boundary points of the higher numerical rangeLinear Algebra and its Applications, 1978
- Singular Values, Diagonal Elements, and ConvexitySIAM Journal on Applied Mathematics, 1977
- Elementary inclusion relations for generalized numerical rangesLinear Algebra and its Applications, 1977
- On Similarity and the Diagonal of a MatrixThe American Mathematical Monthly, 1969
- On the Field of Values of a Square MatrixProceedings of the National Academy of Sciences, 1932