Author Archives: joaquindrut

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. Check out the video and the notes.

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.Check out the video here and the notes.

Definition and properties of the inner product.Check out the video and PDF.

Definition of bases and dimension; part of the series on vector spaces.Check out the video and PDF.

Definition of linear independence and some examples. Part of the series on vector spaces. Check out the video and PDF.

Examples of vector spaces: from 2-component to n-component, real and complex, to function spaces. Check out the video and PDF.

How are vectors and vector spaces defined? We answer that here! Check out the video and the PDF.