Eigenvalue Calculator (2x2)

Find the eigenvalues of a 2x2 matrix using the characteristic polynomial.

Enter a 2x2 matrix:

How It Works

Enter a 2x2 matrix. The eigenvalues are found by solving the characteristic equation det(A - lambda*I) = 0, which becomes a quadratic equation. Results may be real or complex.

Formula

lambda^2 - trace(A)*lambda + det(A) = 0

Frequently Asked Questions

What are eigenvalues?

Eigenvalues are scalars lambda such that Av = lambda*v for some non-zero vector v. They describe how a matrix scales vectors in special directions.

What if the discriminant is negative?

A negative discriminant means the eigenvalues are complex (non-real). This occurs for matrices representing rotations.