Eigenvalue

Under the influence of the A transformation, the vector ξ only increases in scale by a factor of λ. ξ is a eigenvector of A, and λ is the corresponding eigenvalue, which can be measured in experiments. In quantum mechanics theory, many quantities cannot be measured, and of course, this phenomenon also exists in other theoretical fields.

Assuming A is an n-order matrix, if there exists a constant λ and a non-zero n-dimensional vector x such that Ax=λ x, then λ is the eigenvalue of matrix A, and x is the eigenvector of A belonging to eigenvalue λ.

Feature vector

Mathematically, the eigenvector of a linear transformation is a non degenerate vector whose direction remains unchanged under the transformation. The scaling ratio of the vector under this transformation is called its eigenvalue. A linear transformation can usually be fully described by its eigenvalues and eigenvectors. A feature space is a collection of feature vectors with the same eigenvalues. The term 'feature' comes from the German word 'eigen'. Hilbert first used this word in this sense in 1904, and even earlier Helmholtz used it in a related sense. The term 'essence' can be translated as' self ',' specific to ',' distinctive ', or' individual '. This demonstrates how important eigenvalues are for defining specific linear transformations.