This section describes very briefly some of the mathematical concepts used in this book.

Many algorithms used in machine learning such as minimization of a convex loss function, principal component analysis, or least squares regression invariably involve manipulation and transformation of matrices. There are many good books on the subject, from the inexpensive [A:2] to the sophisticated [A:3].

QR decomposition (or QR factorization) is the decomposition of a matrix *A* into a product of an orthogonal matrix *Q* and upper triangular matrix *R*. So, *A=QR* and *Q ^{T}Q=I* [A:4].

The decomposition is unique if *A* is a real, square, and invertible matrix. In the case of a rectangle matrix *A*, *m* by *n* with *m > n*, the decomposition ...

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