Geometrické upotřebení některých pouček o determinantech
Geometrické upotřebení některých pouček o determinantech
Geometrické upotřebení některých pouček o determinantech. [I.]
Geometrické upotřebení některých pouček o determinantechGeometric application of some theorems on determinants. [II.]
G-matrices, -orthogonal matrices, and their sign patterns
A real matrix is a G-matrix if is nonsingular and there exist nonsingular diagonal matrices and such that , where denotes the transpose of the inverse of . Denote by a diagonal (signature) matrix, each of whose diagonal entries is or . A nonsingular real matrix is called -orthogonal if . Many connections are established between these matrices. In particular, a matrix is a G-matrix if and only if is diagonally (with positive diagonals) equivalent to a column permutation of...
Hall exponents of matrices, tournaments and their line digraphs
Let be a square -matrix. Then is a Hall matrix provided it has a nonzero permanent. The Hall exponent of is the smallest positive integer , if such exists, such that is a Hall matrix. The Hall exponent has received considerable attention, and we both review and expand on some of its properties. Viewing as the adjacency matrix of a digraph, we prove several properties of the Hall exponents of line digraphs with some emphasis on line digraphs of tournament (matrices).
Hankel determinants and the Sylvester theorem. (Déterminants de Hankel et théorème de Sylvester.)
Hankel determinants of some sequences of polynomials.
Hankel transforms of linear combinations of Catalan numbers.
Hidden relations for the Smith invariants of a matrix sum
How tight is Hadamard's bound?
Immanant Conversion on Symmetric Matrices
Letr Σn(C) denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C) -> Σn (C) satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB) = dχ·(Φ(Α ) + αΦ(Β)) for all matrices A,В ε Σ„(С) and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С).
Inequalities involving immanants and diagonal products for H-matrices and positive definite matrices
Integer matrices related to Liouville's function
In this note, we construct some integer matrices with determinant equal to certain summation form of Liouville's function. Hence, it offers a possible alternative way to explore the Prime Number Theorem by means of inequalities related to matrices, provided a better estimate on the relation between the determinant of a matrix and other information such as its eigenvalues is known. Besides, we also provide some comparisons on the estimate of the lower bound of the smallest singular value. Such discussion...
Interdependence of some problems arising in generalizing the Marcus-de Oliveira determinantal conjecture
Irreducibility of compound matrices
Kombinatorický důkaz poučky o násobení dvou determinantů
La controverse de 1874 entre Camille Jordan et Leopold Kronecker
Une vive querelle oppose en 1874 Camille Jordan et Leopold Kronecker sur l’organisation de la théorie des formes bilinéaires, considérée comme permettant un traitement « général » et « homogène » de nombreuses questions développées dans des cadres théoriques variés au xixe siècle et dont le problème principal est reconnu comme susceptible d’être résolu par deux théorèmes énoncés indépendamment par Jordan et Weierstrass. Cette controverse, suscitée par la rencontre de deux théorèmes que nous considérerions...
Lehrbuch der Determinanten-Theorie für Studirende [Book]
Linear maps preserving rank 2 on the space of alternate matrices and their applications.