linear algebra

We present an informal outline of how ChatGPT works and describe the underlying mathematical concepts behind it. For instance, graph theory, vector calculus, linear algebra, Markov models, and probabilistic inference are all used in a fundamental way. We will also touch upon some philosophical questions that emerge such as the nature of knowledge, meaning and consciousness. The talk will not be too technical and is suitable for a general audience.

The singular value decomposition (SVD) of a matrix is a fundamental result in linear algebra and its applications in data science.   
It produces good bases for the four fundamental subspaces associated with a real matrix A: the row and column spaces,  the nullspace, and the nullspace of its transpose of A.   The SVD produces a method to find the best approximation of A by matrices of lower rank.  This Theorem has applications to data compression.