I am a first year student at Columbia University studying Mathematics, CS and Statistics. This website will host my projects, notes or papers that I produce during my time at Columbia.
Feel free to contact me at wsb2130@columbia.edu.
Abstract: This paper introduces the geometry and linear-algebraic structure of quadratic forms, focus ing on their symmetric matrix representation, orthogonal diagonalization, definiteness, and role in optimization. We reinterpret classical identities of Diophantus, Brahmagupta, Euler, and Degen as compositions of quadratic forms, leading to the Hurwitz-Radon theorem. The paper also extends these concepts to cubic norm forms and explores applications in statistics. [cite: 358, 359]
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