In linear algebra, the minimal polynomial μA of an n × n {\displaystyle n\times n} matrix A over a field F is the monic polynomial P over F of least degree...

Minimal polynomial can mean: Minimal polynomial (field theory) Minimal polynomial (linear algebra) This disambiguation page lists mathematics articles...

Minimum polynomial can refer to: Minimal polynomial (field theory) Minimal polynomial (linear algebra) This disambiguation page lists articles associated...

Swinnerton-Dyer polynomial. Ring of integers Algebraic number field Minimal polynomial (linear algebra) Weisstein, Eric W. "Algebraic Number Minimal Polynomial". MathWorld...

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

property. Here, "minimal" means that S(V) satisfies the following universal property: for every linear map f from V to a commutative algebra A, there is a...

exactly one which is monic and of minimal degree, called the minimal polynomial of x. The minimal polynomial of an algebraic element x of L is irreducible...

especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more indeterminates...

Linear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b...

characteristic polynomial of a matrix or linear operator contains information about the operator's eigenvalues. The minimal polynomial of an algebraic element...

In algebra, a multilinear polynomial is a multivariate polynomial that is linear (meaning affine) in each of its variables separately, but not necessarily...

2023-08-23. Retrieved 2023-01-11. Barrera-Mora, Fernando (2023). Linear Algebra: A Minimal Polynomial Approach to Eigen Theory. Walter de Gruyter GmbH & Co KG...

In linear algebra and functional analysis, a projection is a linear transformation P {\displaystyle P} from a vector space to itself (an endomorphism)...

This is a list of polynomial topics, by Wikipedia page. See also trigonometric polynomial, list of algebraic geometry topics. Degree: The maximum exponents...

In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a...

mathematics, a primitive polynomial is the minimal polynomial of a primitive element of the finite field GF(pm). This means that a polynomial F(X) of degree m...

In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field...

In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients...

gives polynomial time, and for c < 1 {\displaystyle c<1} it gives sub-linear time. There are some problems for which we know quasi-polynomial time algorithms...

A polynomial P is annihilating or called an annihilating polynomial in linear algebra and operator theory if the polynomial considered as a function of...

In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of...

field F is algebraically closed if every non-constant polynomial with coefficients in F has a root in F. In other words, a field is algebraically closed if...

values this polynomial takes are the triangular numbers.) Integer-valued polynomials are objects of study in their own right in algebra, and frequently...

set X ⊆ V {\displaystyle X\subseteq V} is linearly independent if and only if X {\displaystyle X} is a minimal element of { Y ⊆ V ∣ X ⊆ Span ⁡ ( Y ) } {\displaystyle...

A} ; this polynomial is the minimal polynomial. Any polynomial which annihilates A {\displaystyle A} (such as the characteristic polynomial) is a multiple...

In linear algebra, two n-by-n matrices A and B are called similar if there exists an invertible n-by-n matrix P such that B = P − 1 A P . {\displaystyle...

similarly as polynomial algebras are used for the study of algebraic varieties, which are solution sets of systems of polynomial equations. Weyl algebras and Lie...

spans the space of polynomials. The set of all linear combinations of a subset S of V, a vector space over K, is the smallest linear subspace of V containing...

theorem of algebra establishes a link between algebra and geometry by showing that a monic polynomial (an algebraic object) in one variable with complex number...

system is always linearly independent. Despite the name, an orthonormal basis is not, in general, a basis in the sense of linear algebra (Hamel basis)....