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This is the first volume of the two-volume book on linear algebra, in the University of Tokyo (UTokyo) Engineering Course. The objective of this volume is to present, from the engineering viewpoint, ...

Dr. James McCaffrey from Microsoft Research presents a complete end-to-end demonstration of the linear support vector regression (linear SVR) technique, where the goal is to predict a single numeric ...

Among other things, the course includes elementary linear algebra, the solution of equation systems, the theory of functions of several variables, including both unconstrained and constrained ...

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Positive definite matrices are widely used in machine learning and probabilistic modeling, especially in applications related to graph analysis and Gaussian models. It is not uncommon that positive ...

If you then find that the dimensions of the vector spaces are different — something that’s much easier to measure — then you know the two spaces can’t be the same. And you figured this out by passing ...

(a) Dense matrices. Variables are often encoded as dense numerical arrays M i,j = M[i,j]. This representation is convenient and well-supported, but also puts a heavy load on the memories of our ...