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.
Explicit Solutions of some Linear Matrix Equations
Exploiting tensor rank-one decomposition in probabilistic inference
We propose a new additive decomposition of probability tables – tensor rank-one decomposition. The basic idea is to decompose a probability table into a series of tables, such that the table that is the sum of the series is equal to the original table. Each table in the series has the same domain as the original table but can be expressed as a product of one- dimensional tables. Entries in tables are allowed to be any real number, i. e. they can be also negative numbers. The possibility of having...
Exponential polynomial inequalities and monomial sum inequalities in -Newton sequences
We consider inequalities between sums of monomials that hold for all p-Newton sequences. This continues recent work in which inequalities between sums of two, two-term monomials were combinatorially characterized (via the indices involved). Our focus is on the case of sums of three, two-term monomials, but this is very much more complicated. We develop and use a theory of exponential polynomial inequalities to give a sufficient condition for general monomial sum inequalities, and use the sufficient...
Exponential Riordan arrays and permutation enumeration.
Exponents of two-colored digraphs
We consider the primitive two-colored digraphs whose uncolored digraph has vertices and consists of one -cycle and one -cycle. We give bounds on the exponents and characterizations of extremal two-colored digraphs.
Expression de comme quotient de deux déterminants
Expression of a tensor commutation matrix in terms of the generalized Gell-Mann matrices.