We show how to simply construct two vector spaces of pencils that generalize the companion forms of $P$, and prove that almost all of these pencils are linearizations for $P$.Expand

In this paper several useful classes of structured polynomials (e.g., palindromic, even, odd) are identified and the relationships between them explored.Expand

A standard way of dealing with a matrix polynomial $P(\lambda)$ is to convert it into an equivalent matrix pencil—a process known as linearization.Expand

Abstract The concept of linearization is fundamental for theory, applications, and spectral computations related to matrix polynomials. However, recent research on several important classes of… Expand

The standard way of solving the polynomial eigenvalue problem of degree $m$ in $n\times n$ matrices is to “linearize” to a pencil in vector space $\mathbb{DL}(P)$ of pencils recently identified and studied by Mackey and Mehrmann.Expand

A standard way of treating the polynomial eigenvalue problem $P(\lambda)x = 0$ is to convert it into an equivalent matrix pencil—a process known as linearization.Expand

A standard way of dealing with a regular matrix polynomial P (λ) is to convert it into an equivalent matrix pencil - a process known as linearization. Two vector spaces of pencils L1(P ) and L2(P )… Expand

Alternating matrix polynomials, that is, polynomials whose coefficients alternate between symmetric and skew-symmetric matrices, generalize the notions of even and odd scalar polynomials. We… Expand

We study the structure in eigenvalues, eigenvectors, and singular values that persists across a wide range of scalar products of a scalar product when the product is factored.Expand

We extend the definition of hyperbolic matrix polynomial in a way that relaxes the requirement of definiteness of the leading coefficient matrix, yielding what we call definite polynomials.Expand