Eigenvector Calculator

Find the eigenvectors and eigenvalues of a 2x2 matrix.

Enter 2x2 Matrix

Eigenvalue 1

λ₁ = 5.0000

Eigenvector 1

v₁ = [-0.8944, -0.4472]

Eigenvalue 2

λ₂ = 2.0000

Eigenvector 2

v₂ = [-0.7071, 0.7071]

Matrix Properties

Trace

7.0000

Determinant

10.0000

Discriminant

9.0000

About Eigenvectors

An eigenvector v of a matrix A satisfies Av = λv, where λ is the corresponding eigenvalue. The eigenvector points in a direction that is only scaled (not rotated) by the matrix transformation.

Characteristic equation: det(A - λI) = 0