Mathematically, the linearly transformed eigenvector (eigenvector) is a non-degenerate vector whose direction is unchanged under the transformation. The scale at which this vector is scaled under this transformation is called its eigenvalue (eigenvalue). A linear transformation can usually be fully described by its eigenvalues and eigenvectors. A feature space is a collection of feature vectors of the same feature value. The word "feature" comes from the German eigen. In 1904, Hilbert first used the term in this sense, and earlier Helmholtz used the term in a relevant sense. The word eigen can be translated as "own", "specifically", "characterized", or "individual". This shows how important eigenvalues are for defining a particular linear transformation.

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