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Machine Learning: End-to-End guide for Java developers

You're reading from   Machine Learning: End-to-End guide for Java developers Data Analysis, Machine Learning, and Neural Networks simplified

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Product type Course
Published in Oct 2017
Publisher Packt
ISBN-13 9781788622219
Length 1159 pages
Edition 1st Edition
Languages
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Authors (2):
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Krishna Choppella Krishna Choppella
Author Profile Icon Krishna Choppella
Krishna Choppella
Uday Kamath Uday Kamath
Author Profile Icon Uday Kamath
Uday Kamath
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Toc

Appendix A. Linear Algebra

Linear algebra is of primary importance in machine learning and it gives us an array of tools that are especially handy for the purpose of manipulating data and extracting patterns from it. Moreover, when data must be processed in batches as in much machine learning, great runtime efficiencies are gained from using the "vectorized" form as an alternative to traditional looping constructs when implementing software solutions in optimization or data pre-processing or any number of operations in analytics.

We will consider only the domain of real numbers in what follows. Thus, a vector Linear Algebra represents an array of n real-valued numbers. A matrix Linear Algebra is a two-dimensional array of m rows and n columns of real-valued numbers.

Some key concepts from the foundation of linear algebra are presented here.

Vector

The vector x (lowercase, bold, by convention; equivalently, Vector) can be thought of as a point in n-dimensional space. Conventionally, we mean column-vector...

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