eigenvector

[ahy-guhn-vek-ter]

noun

Mathematics.

1. characteristic vector.

eigenvector

/ ˈaɪɡənˌvɛktə /

noun

1. maths physics a vector x satisfying an equation A x = λ x , where A is a square matrix and λ is a constant

Word History and Origins

Origin of eigenvector¹

First recorded in 1955–60, eigenvector is from the German word Eigenvektor

Example Sentences

A key innovation in the study is the introduction of a new weighting function based on the phase information of the first eigenvector -- a special vector that, when multiplied by the matrix, results in a scaled version of the original vector.

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In general, a ray of points emanating from the origin can be stretched and rotated by a transformation encoded by a matrix, but in a special direction called the eigenvector, the transformation is limited to stretching or shrinking.

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The Perron-Frobenius theorem states that for a square matrix with all positive entries, there is a unique largest real eigenvalue and that its corresponding eigenvector has positive x and y coordinates.

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The recent Wired article notes that the Stitch Fix data science team uses “something called eigenvector decomposition, a concept from quantum mechanics, to tease apart the overlapping ‘notes’ in an individual’s style.”

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As many people pointed out on Twitter, eigenvector decomposition is just a regular old linear algebra technique.

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