Eigenvalues

Under the action of the A transform, the vector ξ becomes only the original λ times on the scale. Weighing ξ is a eigenvector of A, λ is the corresponding eigenvalue (eigenvalue), which is the amount that can be measured (in experiment), and correspondingly in quantum mechanics theory, many quantities cannot be measured, of course This phenomenon is also found in other theoretical fields.

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

Feature vector

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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