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


Homotopy Continuation

Grobner Bases

Cylindrical Algebraic Decomposition (CAD)



Linear algebra but wih rings instead of fields. You can’t divide by scalars anymore.

Resources msolve. a C library for grobner basis and root calculations. Intresting