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 Hopf fibration double covers circle bundle of sphere
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 Why is a² + b² ≥ 2ab ?
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 The CauchySchwarz inequality and the Lagrange identity
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Category Archives: Group theory
Hopf fibration double covers circle bundle of sphere
Two days ago, I gave a seminar talk on Chern‘s proof of the generalized GaussBonnet theorem. Here I record the answer to a question asked by one of my colleague during the talk. Although not directly related to the proof … Continue reading
Posted in Algebra, Differential geometry, Group theory
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The CauchySchwarz inequality and the Lagrange identity
The classical Lagrange identity is the following: This can be proven by expanding and separating the terms into the crossterms part and the non crossterms part. The Lagrange identity implies the CauchySchwarz inequality in . And when , this can … Continue reading
Posted in Algebra, Group theory, Inequalities, Linear Algebra
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