Das verallgemeinerte Inverse eines linearen Operators in Vektorräumen mit nicht ausgearteter Hermitescher Metrik über einenm kommutativen Körper.
Erratum: “Lower bounds for some factorable matrices" [Int. J. Math. Math. Sci. 2006, No. 14, Article ID 76135 (2006; Zbl pre05231649)].
Estimates for absolute values of matrix functions.
Falseness of the finiteness property of the spectral subradius
We prove that there exist infinitely may values of the real parameter α for which the exact value of the spectral subradius of the set of two matrices (one matrix with ones above and on the diagonal and zeros elsewhere, and one matrix with α below and on the diagonal and zeros elsewhere, both matrices having two rows and two columns) cannot be calculated in a finite number of steps. Our proof uses only elementary facts from the theory of formal languages and from linear algebra, but it is not constructive...
From Eckart and Young approximation to Moreau envelopes and vice versa
In matricial analysis, the theorem of Eckart and Young provides a best approximation of an arbitrary matrix by a matrix of rank at most r. In variational analysis or optimization, the Moreau envelopes are appropriate ways of approximating or regularizing the rank function. We prove here that we can go forwards and backwards between the two procedures, thereby showing that they carry essentially the same information.
Gegenbauer matrix polynomials and second order matrix differential equations.
Generalized approximation numbers
Generalized induced norms
Let be a norm on the algebra of all matrices over . An interesting problem in matrix theory is that “Are there two norms and on such that for all ?” We will investigate this problem and its various aspects and will discuss some conditions under which .
Generalized numerical ranges of permanental compounds arising from quantum systems of bosons.
Indefinite numerical range of matrices
The point equation of the associated curve of the indefinite numerical range is derived, following Fiedler’s approach for definite inner product spaces. The classification of the associated curve is presented in the indefinite case, using Newton’s classification of cubic curves. Illustrative examples of all the different possibilities are given. The results obtained extend to Krein spaces results of Kippenhahn on the classical numerical range.
Inequalities on the singular values of an off-diagonal block of a Hermitian matrix.
Integral representation of the Drazin inverse.
Interdependence of some problems arising in generalizing the Marcus-de Oliveira determinantal conjecture
Iterations of concave maps, the Perron-Frobenius theory, and applications to circle packings.
Krein spaces numerical ranges and their computer generation.
-norm of iterates and the spectral radius of matrices
Lower bounds for some factorable matrices.
Lower bounds for the spectral norm.
Majorants of matrix norms and spectrum localization
Maps preserving spectral radius, numerical radius, spectral norm.