Formes quadratiques multiplicatives et variétés algébriques
Formes quadratiques réelles semi-définies. Démonstration élémentaire du critère des mineurs principaux.
Formes quadratiques sur un semi-groupe involutif.
Forms of the Cayley-Hamilton theorem for generalized systems.
Formulae for General Reproductive Solutions of Certain Matrix Equations
Forty necessary and sufficient conditions for regularity of interval matrices: A survey.
Fredholm determinants
The article provides with a down to earth exposition of the Fredholm theory with applications to Brownian motion and KdV equation.
Free generalized gamma convolutions.
Free ℤ-module
In this article we formalize a free ℤ-module and its rank. We formally prove that for a free finite rank ℤ-module V , the number of elements in its basis, that is a rank of the ℤ-module, is constant regardless of the selection of its basis. ℤ-module is necessary for lattice problems, LLL(Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattice [15]. Some theorems in this article are described by translating theorems in [21] and [8] into theorems of Z-module.
Freie Auflösungen äusserer Potenzen.
Fröhlich's local quadratic forms.
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.
From equivalent linear equations to Gauss-Markov theorem.
From geometry to invertibility preservers
We characterize bijections on matrix spaces (operator algebras) preserving full rank (invertibility) of differences of matrix (operator) pairs in both directions.
Full rank factorization and the Flanders theorem.
Further determinant identities related to classical root systems
By introducing polynomials in matrix entries, six determinants are evaluated which may be considered extensions of Vandermonde-like determinants related to the classical root systems.
Further results on the Craig-Sakamoto equation.
Further results on the reverse order law for -inverse and -inverse of a matrix product.
Fuzzy transforms in image compression and fusion
An overview of direct and inverse fuzzy transforms of three types is given and applications to data processing are considered. The construction and some important properties of fuzzy transforms are presented on the theoretical level. Three applications of -transform to data processing have been chosen: compressional and reconstruction of data, removing noise and data fusion. All of them successively exploit the filtering property of the inverse fuzzy transform.