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[Music] welcome back so were coding up different uses of the singular value decomposition in Python and now were ready to talk about how to use the SVD to compute the principal component analysis or PCA and PCA again is one of the most important techniques in the statistical analysis of high dimensional data so if you have big data and you want to understand what are the kind of dominant directions of variants in that data then the principal component analysis is going to be the right tool for that and were going to compute it using the singular value decomposition so as I always like to say if youre going to use a mathematical technique in the real world on a real problem its a good idea to check out how it works on a toy problem where you know the answer first so thats what were going to do here is we are going to essentially create a data set that is you know Gaussian distributed data with some degrees so some directions of high variance and directions of low variance and th