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An eigenvector of a square matrix A is a non-zero vector v, When A v = λ v, the λ is called the eigenvalue of A corresponding to v.

All eigenvalues and eigenvectors satisfy the equation Ax = λx for a given square matrix A.

The online Eigenvectors and Eigenvalues Calculator can get |A|, Singular Matrix (A - c×I), Trace of A, Eigen Value of the matrix A

For example

For matrix

the vector

is an eigenvector with eigenvalue 2.

On the other hand the vector

is not an eigenvector, since

and this vector is not a multiple of the original vector v.