Nonlinear Algebra
By nonlinear algebra I mean things relating to multivariate polynomials
Linear modelling of nonlinear systems
Vandermonde Matrix
The big question: Linear in what? You can always determine a polynomial as a linear algebra problem given sample points. A polynomial can bethought of as linear in it’s coefficients
Companion Matrix
wiki A matrix designed to have characterstic polynomial
Sylvester matrix
Univariate Polynomials
We’re really good at these. Fundamental theorem of algebra
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Homotopy Continuation
Grobner Bases
Cylindrical Algebraic Decomposition (CAD)
NLSAT
Modules
Linear algebra but wih rings instead of fields. You can’t divide by scalars anymore.