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eigenvectors and eigenvalues
Sign in to saveAlso known as eigenvalues and eigenvectors, eigenvalue and eigenvector, eigenvector and eigenvalue, eigen, matrix eigenvectors
vectors that map to their scalar multiples, and the associated scalars
Eigenvectors are special directions in a mathematical space that don't change direction when a transformation is applied to them—they only get stretched or shrunk by a fixed amount called an eigenvalue. These concepts matter because they help us understand how transformations work, and they appear throughout science and engineering in applications like analyzing vibrations, compressing images, and predicting long-term behavior of systems.
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In linear algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a (nonzero) vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector
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