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Numpy Beginner's Guide (Update)

Numpy Beginner's Guide (Update)

By : Ivan Idris
2 (1)
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Numpy Beginner's Guide (Update)

Numpy Beginner's Guide (Update)

2 (1)
By: Ivan Idris

Overview of this book

This book is for the scientists, engineers, programmers, or analysts looking for a high-quality, open source mathematical library. Knowledge of Python is assumed. Also, some affinity, or at least interest, in mathematics and statistics is required. However, I have provided brief explanations and pointers to learning resources.
Table of Contents (16 chapters)
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14
C. NumPy Functions' References
15
Index

Singular value decomposition

Singular value decomposition (SVD) is a type of factorization that decomposes a matrix into a product of three matrices. The SVD is a generalization of the previously discussed eigenvalue decomposition. SVD is very useful for algorithms such as the pseudo inverse, which we will discuss in the next section. The svd() function in the numpy.linalg package can perform this decomposition. This function returns three matrices U, , and V such that U and V are unitary and contains the singular values of the input matrix:

Singular value decomposition

The asterisk denotes the Hermitian conjugate or the conjugate transpose. The complex conjugate changes the sign of the imaginary part of a complex number and is therefore not relevant for real numbers.

Note

A complex square matrix A is unitary if A*A = AA* = I (the identity matrix). We can interpret SVD as a sequence of three operations—rotation, scaling, and another rotation.

We already transposed matrices in this book. The transpose...

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