Evaluations of some determinants of matrices related to the Pascal triangle.
Evasion and prediction - the Specker phenomenon and Gross space.
Even and odd tournament matrices with minimum rank over finite fields.
Exact Solution of Linear Equations Using P-Adic Expansions
Examples Illustrating some Aspects of the Weak Deligne-Simpson Problem
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...
Existence and construction of two-dimensional invariant subspaces for pairs of rotations
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...
Existence et unicité du maximum d'une forme linéaire sur un ensemble de matrices diagonales
Existence of matrices with prescribed entries.
Existence theorems for commutative diagrams.
Existenzsätze in der Theorie der Matrizen und lineare Kontrolltheorie.
Expansion of (n -1)-Rowed Sub-Determinants.
Explicit forms of block matrices in unbalanced cross classification
Explicit formulas for the constituent matrices. Application to the matrix functions
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.
Explicit inverse of an interval matrix with unit midpoint.
Explicit inverse of the Pascal matrix plus one.
Explicit inverses of several tridiagonal matrices.
Explicit polar decomposition of companion matrices.
Explicit polar decomposition of complex matrices.
Explicit solution of the inverse eigenvalue problem of real symmetric matrices and its application to electrical network synthesis.
Explicit solutions of infinite linear systems associated with group inverse endomorphisms
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.