Mathematically, an eigenvector of a linear transformation is a non-degenerate vector whose direction is invariant under the transformation. The scale to which the vector is scaled under the transformation is called its eigenvalue. A linear transformation can usually be fully described by its eigenvalues ​​and eigenvectors. An eigenspace is the set of eigenvectors with the same eigenvalue. The word "characteristic" comes from the German word eigen. Hilbert first used the word in this sense in 1904, and Helmholtz used it earlier in a related sense. The word eigen can be translated as "own", "specific to", "characteristic", or "individual". This shows how important eigenvalues ​​are in defining a particular linear transformation.