Harvard AM205 video 2.9 - Householder triangularization

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Harvard Applied Math 205 is a graduate-level course on scientific computing and numerical methods. This video introduces householder triangularization, a method for computing the QR decomposition of a matrix.

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In my opinion in video is missing explanation of effective multiplication by H matrices
I dont want to use extra O(n^2) space for H matrices and high school matrix multiplication because it will be too costly
Moreover I would like to use Householder reflections to Hessenberg reduction and
for generating orthogonal polynomials

holyshit