Applications of Linear Algebra
As linear algebra is the mathematics of data, the tools of linear algebra are used in many
domains. In his classical book on the topic titled Introduction to Linear Algebra, Gilbert Strang
provides a chapter dedicated to the applications of linear algebra. In it, he demonstrates specific
mathematical tools rooted in linear algebra. Briefly they are:
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Matrices in Engineering, such as a line of springs.
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Graphs and Networks, such as analyzing networks.
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Markov Matrices, Population, and Economics, such as population growth.
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Linear Programming, the simplex optimization method.
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Fourier Series: Linear Algebra for functions, used widely in signal processing.
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Linear Algebra for statistics and probability, such as least squares for regression.
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Computer Graphics, such as the various translation, rescaling and rotation of images.
Another interesting application of linear algebra is that it is the type of mathematics used
by Albert Einstein in parts of his theory of relativity. Specifically tensors and tensor calculus.
He also introduced a new type of linear algebra notation to physics called Einstein notation, or
the Einstein summation convention.
Further Reading
This section provides more resources on the topic if you are looking to go deeper.
Books
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Introduction to Linear Algebra, 2016.
http://amzn.to/2j2J0g4
Numerical Linear Algebra, 1997.
http://amzn.to/2kjEF4S
Linear Algebra and Matrix Analysis for Statistics, 2014.
http://amzn.to/2A9ceNv
Articles
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Linear Algebra on Wikipedia.
https://en.wikipedia.org/wiki/Linear_algebra
Linear Algebra Category on Wikipedia.
https://en.wikipedia.org/wiki/Category:Linear_algebra
1.7. Summary
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6
Linear Algebra List of Topics on Wikipedia.
https://en.wikipedia.org/wiki/List_of_linear_algebra_topics
LAPACK on Wikipedia.
https://en.wikipedia.org/wiki/LAPACK
Basic Linear Algebra Subprograms on Wikipedia.
https://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms
Automatically Tuned Linear Algebra Software on Wikipedia.
https://en.wikipedia.org/wiki/Automatically_Tuned_Linear_Algebra_Software
Einstein notation on Wikipedia.
https://en.wikipedia.org/wiki/Einstein_notation
Mathematics of general relativity on Wikipedia.
https://en.wikipedia.org/wiki/Mathematics_of_general_relativity
Summary
In this tutorial, you discovered a gentle introduction to linear algebra from a machine learning
perspective. Specifically, you learned:
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Linear algebra is the mathematics of data.
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Linear algebra has had a marked impact on the field of statistics.
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Linear algebra underlies many practical mathematical tools, such as Fourier series and
computer graphics.
1.7.1
Next
In the next chapter you will discover why linear algebra is important to machine learning.