I show how to use the inner product to orthogonalize monomials and obtain the Hermite polynomials as a result, using Gram-Schmidt orthogonalization.
Details on Gaussian integrals and more on the Feynman trick in a future issue.

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Definition of orthogonal bases. This video goes beyond vector spaces, using the inner product to define orthogonal bases in spaces of common vectors and functions.
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Definition and properties of the inner product.
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Definition of bases and dimension; part of the series on vector spaces.
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Definition of linear independence and some examples.
Part of the series on vector spaces.

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Examples of vector spaces: from 2-component to n-component, real and complex, to function spaces.

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How are vectors and vector spaces defined? We answer that here!

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