Eigenvalue and Eigenvector Calculator

Matrix A =

Identity Matrix I =

c =

Number matrix (Z=c×I)

|A| =

The trace of the matrix A =

Singular Matrix(A - c×I) =

|A - c×I| =

Eigenvalue (c1) =

Eigenvalue (c2) =

The value of c1 in the eigenvector x1 =

The value of c1 in the eigenvector x2 =

The value of c2 in the eigenvector x1 =

The value of c2 in the eigenvector x2 =

Eigenvalue

Under the action of A transformation, the vector ξ is only changed to λ times the original in scale. ξ is called an eigenvector of A, and λ is the corresponding eigenvalue (eigenvalue), which is a quantity that can be measured (in experiments). Correspondingly, in quantum mechanics theory, many quantities cannot be measured. Of course, this phenomenon also exists 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 called the eigenvalue of the matrix A, and x is the eigenvector of A belonging to the eigenvalue λ.

Eigenvector

In mathematics, the eigenvector (eigenvector) of a linear transformation is a non-degenerate vector whose direction remains unchanged under the transformation. The scale of the vector under this transformation is called its eigenvalue (eigenvalue). A linear transformation can usually be completely described by its eigenvalue and eigenvector. The eigenspace is the set of eigenvectors with the same eigenvalue. The word "eigen" 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 for defining specific linear transformations.