Related papers: LU decomposition of totally nonnegative matrices
In this paper, we establish a uniqueness theorem for algebraically nondegenerate meromorphic maps of C^m into C P^n and slowly moving hypersurfaces Q_j in C P^n, j=1,...,q in (weakly) general position, where q depends effectively on n and…
Singular value decompositions of matrices are widely used in numerical linear algebra with many applications. In this paper, we extend the notion of singular value decompositions to finite complexes of real vector spaces. We provide two…
We prove that if a unitary representation of a connected Lie group has the property that no nonozero vector is fixed by any nontrival normal connected subgroup, then the matrix coefficients decay to zero at Adjoint-infinity.
In the present paper we introduce a notion of $G-$decompositions of matrices. Main result of the paper is that a symmetric matrix $A_m$ has a $G-$decomposition in the class of stochastic (resp. substochastic) matrices if and only if $A_m$…
Orthogonal decomposition of tensors is a generalization of the singular value decomposition of matrices. In this paper, we study the spectral theory of orthogonally decomposable tensors. For such a tensor, we give a description of its…
We give a short proof of a recent result by Bernik, Mastnak, and Radjavi, stating that an irreducible group of complex matrices with nonnegative diagonal entries is diagonally similar to a group of nonnegative monomial matrices. We also…
In this paper, we prove that if the matrix of the linear system is symetric, the Cholesky decomposition can be obtained from the Gauss elimination method without pivoting, without proving that the matrix of the system is positive definite.
We prove that a large family of graphs which are decomposable with respect to the modular decomposition can be reconstructed from their collection of vertex-deleted subgraphs.
The principal objective of this paper is to determine the structure of $n$-Lie derivations ($n\geq 3$) on generalized matrix algebras.It is shown that under certain mild assumptions, every $n$-Lie derivation can be decomposed into the sum…
We generalize a fundamental theorem on positive matrix semigroups stating that each component is either strictly positive for all times or identically zero ("L\'evy's Theorem"). Our proof of this fact that does not require the matrices to…
In this paper, a new general decomposition theory inspired from modular graph decomposition is presented. Our main result shows that, within this general theory, most of the nice algorithmic tools developed for modular decomposition are…
The idea of decomposing a matrix into a product of structured matrices such as triangular, orthogonal, diagonal matrices is a milestone of numerical computations. In this paper, we describe six new classes of matrix decompositions,…
Seymour's famous decomposition theorem for regular matroids states that any totally unimodular (TU) matrix can be constructed through a series of composition operations called $k$-sums starting from network matrices and their transposes and…
Let A be an algebra whose group of units U(A) satisfies a Laurent polynomial identity (LPI). We establish conditions on these polynomials in such a way that nil-generated algebras and group algebras with torsion groups over infinite fields…
In polarization optics, an important role play Mueller matrices -- real four-dimensional matrices which describe the effect of action of optical elements on the polarization state of the light, described by 4-dimensional Stokes vectors. An…
In this note, we aim to prove the finite semi-algebraic chamber decomposition theorem for K-semi(poly)stability under the assumption of the log boundedness of K-semistable degenerations. This boundedness assumption is naturally arising from…
We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.
We establish a Lichnerowicz type vanishing theorem for non-compact spin manifolds admiting proper cocompact actions, when the action group is unimodular.
A new proof of the decomposition theorem is established using a relation with a version of the local purity theorem of Deligne and Gabber adapted to complex algebraic varieties.
An invariant theoretic characterization of subdiscriminants of matrices is given. The structure as a module over the special orthogonal group of the minimal degree non-zero homogeneous component of the vanishing ideal of the variety of real…