Eigenvector
/ˈaɪɡənˌvɛktər/noun
A vector that remains parallel to its original direction after a linear transformation is applied.
In the context of linear transformations, an eigenvector of a matrix is a vector that does not change its direction.
Often appears as...
- eigenvalue problem
- principal component analysis
Usage tips
Formal
linear transformation, matrix theory, eigenvalue problem
Definition 1 of 1
Pro Tip 1/3Understanding Context
An eigenvector is always associated with an eigenvalue, which represents the factor by which the eigenvector is scaled.
In a matrix transformation, the direction of the eigenvector remains unchanged.
Pro Tip 2/3Application in PCA
In data analysis, eigenvectors help identify the principal components that capture the most variance in the data.
This technique is widely used for reducing dimensionality in machine learning.
Pro Tip 3/3Relationship to Eigenvalues
An eigenvector always has an eigenvalue; the value indicates the amount of stretch or compression along that direction.
For example, if the eigenvalue is 2, the eigenvector is stretched to twice its length.
Compare with
eigenvaluematrixscalar
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