Autovalores 2×2

This calculator finds the eigenvalues of a 2x2 matrix quickly and accurately. Simply enter the four matrix elements (a, b, c, d) and click calculate. The result displays the two eigenvalues, real or complex, as appropriate. The tool is ideal for students and professionals who need a reliable calculation without manual errors.

The calculation is based on the characteristic equation λ² − tr·λ + det = 0, where tr is the trace (a + d) and det is the determinant (ad − bc). The eigenvalues are the roots of this quadratic equation: λ = (tr ± √(tr² − 4det))/2. The calculator performs these steps automatically, showing the discriminant and the type of eigenvalues (distinct real, repeated real, or complex).

Use this calculator in Linear Algebra courses, when solving systems of linear differential equations, or in engineering and physics applications involving matrix diagonalization. For example, when analyzing the stability of a dynamical system or calculating vibration modes. The tool is also useful for checking exercise results and avoiding calculation mistakes.

Caution: Ensure the entered values are correct, especially the signs of the elements. The calculator handles real numbers; if the discriminant is negative, the eigenvalues will be complex conjugates. Remember that complex eigenvalues indicate oscillatory behavior in dynamical systems. Always interpret the results in the context of your problem.