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...

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

minimal polynomial μA of an n × n matrix A over a field F is the monic polynomial P over F of least degree such that P(A) = 0. Any other polynomial Q with...

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

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"...

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

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

that this number can be computed in polynomial time from the determinant of a submatrix of the Laplacian matrix of the graph; specifically, the number...

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

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...

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

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

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...

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

satisfies its own characteristic equation. The characteristic polynomial of an n × n matrix A is defined as p A ( λ ) = det ( λ I n − A ) {\displaystyle...

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...

has a nonzero determinant, and the eigenvalues of a square matrix are the roots of a polynomial determinant. In geometry, matrices are widely used for specifying...

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...

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

mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order n {\displaystyle...

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

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...

Newton polynomial, named after its inventor Isaac Newton, is an interpolation polynomial for a given set of data points. The Newton polynomial is sometimes...