April 2017
Intermediate to advanced
532 pages
12h 39m
English
book
Machine Learning with Spark - Second Edition
by Rajdeep Dua, Brian O'Neill, Stephen Boesch, Manpreet Singh Ghotra, Nick Pentreath
Content preview from Machine Learning with Spark - Second Edition
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Eigenvalues and eigenvectors
Ax = b is a linear equation which emerges from static problems. Eigenvalues, on the other hand, are used for dynamic problems. Let's consider A as a matrix with x as a vector; we will now solve the new equation in linear algebra, Ax= λx.
As A multiplies x, the vector x changes its direction. But there are certain vectors in the same direction as Ax-these are known as eigenvectors, for which the following equation holds good:
Ax= λx
In the last equation, vector Ax is lambda times the vector x, and λ is known as eigenvalue. Eigenvalue λ gives the direction of a vector-if it is reversed, or is in the same direction.
Ax= λx also conveys that det(A - λI) = 0, where I is the identity matrix. This determines n eigenvalues. ...
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