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Mathematical Challenge Eight: Beyond Convex Optimization * Can linear algebra be replaced by algebraic geometry in a systematic way?

Never heard about it before, but I never knew there was a potential alternative to linear algebra.

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This proposal is different from what's being discussed here. Algebraic geometry is, roughly speaking, about understanding the solutions to systems of polynomial equations, while linear algebra is much simpler and gives complete descriptions of the solutions of systems of linear equations. Geometric algebra is a framework for working with vectors and related objects in an algebraic way---one can "multiply" two vectors together and extract information from this.

Thank you for the correction. I misunderstood.

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