Related papers: The Characteristic Polynomial of Projections

The typical definition of the characteristic polynomial seems totally ad hoc to me. This note gives a canonical construction of the characteristic polynomial as the minimal polynomial of a "generic" matrix. This approach works not just for…

Given a multiarrangement of hyperplanes we define a series by sums of the Hilbert series of the derivation modules of the multiarrangement. This series turns out to be a polynomial. Using this polynomial we define the characteristic…

We observe that the characteristic polynomial of a linearly perturbed semidefinite matrix can be used to give the convergence rate of alternating projections for the positive semidefinite cone and a line. As a consequence, we show that such…

We generalize the differential dimension polynomial from prime differential ideals to characterizable differential ideals. Its computation is algorithmic, its degree and leading coefficient remain differential birational invariants, and it…

There is a digraph corresponding to every square matrix over $\mathbb{C}$. We generate a recurrence relation using the Laplace expansion to calculate the characteristic, and permanent polynomials of a square matrix. Solving this recurrence…

We study the characteristic polynomial of random permutation matrices following some measures which are invariant by conjugation, including Ewens' measures which are one-parameter deformations of the uniform distribution on the permutation…

We study correlation functions of the characteristic polynomials in coupled matrix models based on the Schur polynomial expansion, which manifests their determinantal structure.

In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the…

We give a formula for computing the characteristic polynomial for certain hyperplane arrangements in terms of the number of bipartite graphs of given rank and cardinality.

In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ…

The problem "A general characterization of uniqueness polynomial for non-critically injective polynomials" has been remained open since the last two decades. In this paper, we explore this open problem. To this end, we initiate a new…

In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the…

Consider a finite collection of affine hyperplanes in $\mathbb R^d$. The hyperplanes dissect $\mathbb R^d$ into finitely many polyhedral chambers. For a point $x\in \mathbb R^d$ and a chamber $P$ the metric projection of $x$ onto $P$ is the…

We consider projections of points onto fundamental chambers of finite real reflection groups. Our main result shows that for groups of type $A_n$, $B_n$, and $D_n$, the coefficients of the characteristic polynomial of the reflection…

A univariate trace polynomial is a polynomial in a variable x and formal trace symbols Tr(x^j). Such an expression can be naturally evaluated on matrices, where the trace symbols are evaluated as normalized traces. This paper addresses…

An integral quadratic polynomial (with positive definite quadratic part) is called almost universal if it represents all but finitely many positive integers. In this paper, we provide a characterization of almost universal ternary quadratic…

In this article, we focus on the characteristic polynomial of a graph containingloops, but without multiple edges. We present a relationship between thecharacteristic polynomial of a graph with loops and the graph obtained byremoving all…

We study the characteristic polynomial of Haar distributed random unitary matrices. We show that after a suitable normalization, as one increases the size of the matrix, powers of the absolute value of the characteristic polynomial as well…

Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…

We analyze the precision of the characteristic polynomial of an $n\times n$ p-adic matrix A using differential precision methods developed previously. When A is integral with precision O(p^N), we give a criterion (checkable in time…