Add to ORKGIn this note we develop a new way of formulating the notions of minimal basis and minimal indices, based on the concept of a filtration of a vector space. The goal is to provide useful new tools for working with these important concepts, as well as to gain deeper insight into their fundamental nature. This approach also readily reveals a strong minimality property of minimal indices, from which follows a characterization of the vector polynomial bases in rational vector spaces. The effectiveness of this new formulation is further illustrated by proving two fundamental properties: the invariance of the minimal indices of a matrix polynomial under field extension, and the direct sum property of minimal indices
AbstractWe study the problem of eliminating the minimal indices (the indices of a minimal polynomial...
The concept of linearization is fundamental for theory, applications, and spectral computations rela...
In linear algebra, the minimal polynomial of an n-by-n matrix A over a field F is the monic polynomi...
In this note we develop a new way of formulating the notions of minimal basis and minimal indices, b...
In this note we develop a new way of formulating the notions of minimal basis and minimal indices, b...
Polynomial minimal bases of rational vector subspaces are a classical concept that plays an importan...
Minimal bases of rational vector spaces are a well-known and important tool in systems theory. If mi...
Minimal bases of rational vector spaces are a well-known and important tool in systems theory. If mi...
A standard way of dealing with a matrix polynomial $P(\lambda)$ is to convert it into an equivalen...
Minimal bases of rational vector spaces are a well-known and important tool in systems theory. If m...
A standard way of dealing with a regular matrix polynomial P(¸) is to convert it into an equivalent ...
Abstract. A standard way of dealing with a regular matrix polynomial P (λ) is to convert it into an ...
We want look at the coordinate-free formulation of the idea of a diagonal matrix, which will be call...
This paper studies generic and perturbation properties inside the linear space of polynomial matrice...
Determining whether a number field admits a power integral basis is a classical problem in algebraic...
AbstractWe study the problem of eliminating the minimal indices (the indices of a minimal polynomial...
The concept of linearization is fundamental for theory, applications, and spectral computations rela...
In linear algebra, the minimal polynomial of an n-by-n matrix A over a field F is the monic polynomi...
In this note we develop a new way of formulating the notions of minimal basis and minimal indices, b...
In this note we develop a new way of formulating the notions of minimal basis and minimal indices, b...
Polynomial minimal bases of rational vector subspaces are a classical concept that plays an importan...
Minimal bases of rational vector spaces are a well-known and important tool in systems theory. If mi...
Minimal bases of rational vector spaces are a well-known and important tool in systems theory. If mi...
A standard way of dealing with a matrix polynomial $P(\lambda)$ is to convert it into an equivalen...
Minimal bases of rational vector spaces are a well-known and important tool in systems theory. If m...
A standard way of dealing with a regular matrix polynomial P(¸) is to convert it into an equivalent ...
Abstract. A standard way of dealing with a regular matrix polynomial P (λ) is to convert it into an ...
We want look at the coordinate-free formulation of the idea of a diagonal matrix, which will be call...
This paper studies generic and perturbation properties inside the linear space of polynomial matrice...
Determining whether a number field admits a power integral basis is a classical problem in algebraic...
AbstractWe study the problem of eliminating the minimal indices (the indices of a minimal polynomial...
The concept of linearization is fundamental for theory, applications, and spectral computations rela...
In linear algebra, the minimal polynomial of an n-by-n matrix A over a field F is the monic polynomi...