Nonlinear algebra is the nonlinear analogue to linear algebra, generalizing notions of spaces and transformations coming from the linear setting.[1] Algebraic geometry is one of the main areas of mathematical research supporting nonlinear algebra, while major components coming from computational mathematics support the development of the area into maturity.
The topological setting for nonlinear algebra is typically the Zariski topology, where closed sets are the algebraic sets. Related areas in mathematics are tropical geometry, commutative algebra, and optimization.
^Dolotin, Valery; Morozov, Alexei (2007). Introduction to Non-linear Algebra. World Scientific. ISBN 978-981-270-800-7.
Nonlinearalgebra is the nonlinear analogue to linear algebra, generalizing notions of spaces and transformations coming from the linear setting. Algebraic...
computing efficiently with such models. For nonlinear systems, which cannot be modeled with linear algebra, it is often used for dealing with first-order...
a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems...
In mathematics, a nonlinear eigenproblem, sometimes nonlinear eigenvalue problem, is a generalization of the (ordinary) eigenvalue problem to equations...
polynomial algebras are used for the study of algebraic varieties, which are solution sets of systems of polynomial equations. Weyl algebras and Lie algebras may...
capabilities are general. ASCEND includes nonlinearalgebraic solvers, differential/algebraic equation solvers, nonlinear optimization and modelling of multi-region...
equations. In (numerical) computational mathematics, such as numerical algebraic geometry, candidate solutions are computed algorithmically, but there...
nonlinear, mixed integer, differential and algebraic equations with interfaces to MATLAB, Python, and Julia. Artelys Knitro – large scale nonlinear optimization...
mathematical tool, Colombeau algebras can be said to combine a treatment of singularities, differentiation and nonlinear operations in one framework,...
In time series modeling, a nonlinear autoregressive exogenous model (NARX) is a nonlinear autoregressive model which has exogenous inputs. This means that...
Elimination theory Subresultant Nonlinearalgebra Salmon, George (1885) [1859], Lessons introductory to the modern higher algebra (4th ed.), Dublin, Hodges...
Van der Waerden notation for the notation. In quantum field theory, the nonlinear Dirac equation is a model of self-interacting Dirac fermions. This model...
is a representation of a Lie algebra g {\displaystyle {\mathfrak {g}}} of G in a neighborhood of its origin. A nonlinear realization, when restricted...
linear operators or closed operators, and consideration may be given to nonlinear operators. The study, which depends heavily on the topology of function...
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial...
matrix algebra calculations that are fast and robust. When linear models are not sufficiently accurate to represent the real process nonlinearities, several...
single equations, namely as a: System of linear equations, System of nonlinear equations, System of bilinear equations, System of polynomial equations...
solving nonlinear differential equations exactly; those that are known typically depend on the equation having particular symmetries. Nonlinear differential...
well as nonlinear ones. The former are, for instance, passive filters, active filters, additive mixers, integrators, and delay lines. Nonlinear circuits...
An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time...
In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string...
In linear algebra, it is often important to know which vectors have their directions unchanged by a given linear transformation. An eigenvector (/ˈaɪɡən-/...
measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be...
in Buenos Aires) is an Argentine mathematician known for her work on algebraic geometry, particularly toric geometry, tropical geometry, and their applications...
apart from the elementary symbolic algebra: Expectation algebra, Variance algebra, Covariance algebra, Moment algebra, etc. Considering two random variables...
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