Polynomial matrix information

polynomial matrix or matrix of polynomials is a matrix whose elements are univariate or multivariate polynomials. Equivalently, a polynomial matrix is...

In mathematics, a matrix polynomial is a polynomial with square matrices as variables. Given an ordinary, scalar-valued polynomial P ( x ) = ∑ i = 0 n...

linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as...

In linear algebra, the Frobenius companion matrix of the monic polynomial p ( x ) = c 0 + c 1 x + ⋯ + c n − 1 x n − 1 + x n {\displaystyle p(x)=c_{0}+c_{1}x+\cdots...

In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable...

theorem for polynomials. In statistics, the equation V a = y {\displaystyle Va=y} means that the Vandermonde matrix is the design matrix of polynomial regression...

identity matrix. A matrix polynomial equation is an equality between two matrix polynomials, which holds for the specific matrices in question. A matrix polynomial...

called Hurwitz matrix corresponding to the polynomial p {\displaystyle p} . It was established by Adolf Hurwitz in 1895 that a real polynomial with a 0 >...

In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version...

adjugate of a square matrix A is the transpose of its cofactor matrix and is denoted by adj(A). It is also occasionally known as adjunct matrix, or "adjoint"...

In numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes...

unimodular polynomial matrix is a square polynomial matrix whose inverse exists and is itself a polynomial matrix. Equivalently, a polynomial matrix A is unimodular...

efficient. Determinants are used for defining the characteristic polynomial of a square matrix, whose roots are the eigenvalues. In geometry, the signed n-dimensional...

determinantal matrix representations for bivariate stable polynomials and real zero polynomials. A key tool used to study these is a matrix factorization...

polynomials, of the matrix (with polynomial entries) XIn − A (the same one whose determinant defines the characteristic polynomial). Note that this Smith...

In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a...

blocks of the Sylvester matrix is empty). There is no common convention for the discriminant of a constant polynomial (i.e., polynomial of degree 0). For small...

the eigenvalues of a given matrix. If the matrix is small, we can compute them symbolically using the characteristic polynomial. However, this is often impossible...

positive. This gives the Alexander polynomial. The Alexander polynomial can also be computed from the Seifert matrix. After the work of J. W. Alexander...

side of equation (3) is a polynomial function of the variable λ and the degree of this polynomial is n, the order of the matrix A. Its coefficients depend...

In mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal...

its characteristic polynomial has n {\displaystyle n} distinct roots in F {\displaystyle F} . Let A {\displaystyle A} be a matrix over F {\displaystyle...

matrix is a matrix associated to two univariate polynomials with coefficients in a field or a commutative ring. The entries of the Sylvester matrix of...

_{n}}&\dots &x_{n}^{\lambda _{n}}\end{matrix}}\right]} are alternating polynomials by properties of the determinant. A polynomial is alternating if it changes...

refer to any of the following: Unimodular lattice Unimodular matrix Unimodular polynomial matrix Unimodular form Unimodular group This disambiguation page...