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Results tagged with real-algebraic-geometry
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user 5963
Real algebraic geometry is the study of real solutions to algebraic equations with real coefficients. Its methods are rather different from classical algebraic geometry, which is typically done over an algebraically closed field (like the complex numbers).
1
vote
Hermitian forms with real coefficients
For $d=1$ this is true because $H(z)$ is a bilinear form on $\mathbb{R}^n$ and nonpositive definite by assumption, so it is of the form $H(z) = -\lVert Az\rVert^2$ for some real matrix $A$, and theref …
- 8,501
45
votes
5
answers
9k
views
Real algebraic geometry vs. algebraic geometry
This question is predicated on my understanding that real algebraic geometry (henceforth RAG) is the version of algebraic geometry (AG) one gets when replacing (esp. algebraically closed) fields with …
- 8,501
14
votes
Accepted
Effective algorithm to test positivity
If by effective you mean "is this computable", then yes, the computational versions of Tarski-Seidenberg such as cylindrical algebraic decomposition give you a finite algorithm. (I suppose this is ass …
- 8,501