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# Mathematics

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

## Linear algebra

Many algorithms used in machine learning such as minimization of a convex loss function, principal component analysis, or least squares regression invariably involves 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

The QR decomposition (or the 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 QT 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 ...

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