Evaluations of some determinants of matrices related to the Pascal triangle.
Krattenthaler, C. (2002)
Séminaire Lotharingien de Combinatoire [electronic only]
Jörg Brendle (1995)
Forum mathematicum
Doering, Elizabeth, Michael, T.S., Shader, Bryan L. (2011)
ELA. The Electronic Journal of Linear Algebra [electronic only]
J.D. Dixon (1982)
Numerische Mathematik
Kostov, Vladimir (2001)
Serdica Mathematical Journal
Research partially supported by INTAS grant 97-1644We consider the variety of (p + 1)-tuples of matrices Aj (resp. Mj ) from given conjugacy classes cj ⊂ gl(n, C) (resp. Cj ⊂ GL(n, C)) such that A1 + . . . + A[p+1] = 0 (resp. M1 . . . M[p+1] = I). This variety is connected with the weak Deligne-Simpson problem: give necessary and sufficient conditions on the choice of the conjugacy classes cj ⊂ gl(n, C) (resp. Cj ⊂ GL(n, C)) so that there exist (p + 1)-tuples with trivial centralizers of matrices...
Ernst Dieterich (2009)
Colloquium Mathematicae
By a rotation in a Euclidean space V of even dimension we mean an orthogonal linear operator on V which is an orthogonal direct sum of rotations in 2-dimensional linear subspaces of V by a common angle α ∈ [0,π]. We present a criterion for the existence of a 2-dimensional subspace of V which is invariant under a given pair of rotations, in terms of the vanishing of a determinant associated with that pair. This criterion is constructive, whenever it is satisfied. It is also used to prove that every...
P. Farjot (1976)
Annales scientifiques de l'Université de Clermont. Mathématiques
Ion Zaballa (1986)
Extracta Mathematicae
Rechnoi, V. (2005)
Lobachevskii Journal of Mathematics
Harald K. Wimmer (1974)
Monatshefte für Mathematik
Brian Murphy (1976)
Mathematische Zeitschrift
H. Mikos (1979)
Applicationes Mathematicae
R. Ben Taher, M. Rachidi (2015)
Special Matrices
We present a constructive procedure for establishing explicit formulas of the constituents matrices. Our approach is based on the tools and techniques from the theory of generalized Fibonacci sequences. Some connections with other results are supplied. Furthermore,we manage to provide tractable expressions for the matrix functions, and for illustration purposes we establish compact formulas for both the matrix logarithm and the matrix pth root. Some examples are also provided.
Rohn, Jiri (2011)
ELA. The Electronic Journal of Linear Algebra [electronic only]
Yang, Sheng-Liang, Liu, Zhong-Kui (2006)
International Journal of Mathematics and Mathematical Sciences
Yueh, Wen-Chyuan (2006)
Applied Mathematics E-Notes [electronic only]
van den Driessche, Pauline, Wimmer, Harald K. (1996)
ELA. The Electronic Journal of Linear Algebra [electronic only]
Horn, Roger A., Piazza, Giuseppe, Politi, Tiziano (2009)
ELA. The Electronic Journal of Linear Algebra [electronic only]
Kandić, D.B., Reljin, B.D. (2008)
Mathematical Problems in Engineering
Fernando Pablos Romo (2022)
Czechoslovak Mathematical Journal
The aim of this note is to offer an algorithm for studying solutions of infinite linear systems associated with group inverse endomorphisms. As particular results, we provide different properties of the group inverse and we characterize EP endomorphisms of arbitrary vector spaces from the coincidence of the group inverse and the Moore-Penrose inverse.