Gaussian elimination / RREF
Exact fractions and a full row-operation trace.
Open calculatorMathematics / Free calculator
Eigenvalues & eigenvectors
Explore real or complex eigenvalues and eigenvectors of real 2×2 and 3×3 matrices, with verification steps.
01 Your inputs
02 Your result
Enter your values and select Calculate.
The method
A worked example
For [2 1 0; 1 2 0; 0 0 4], eigenvalues are 1, 3, and 4. Corresponding unit vectors are proportional to [1 −1 0], [1 1 0], and [0 0 1]. Each satisfies Av = λv.
Assumptions & limits
Real 2×2 or 3×3 input only. Eigenvalues and vectors are floating-point approximations; 3×3 eigenspaces use a 10⁻⁹ tolerance on the scaled matrix. Nearly repeated roots and ill-conditioned matrices require independent review. A small residual does not guarantee eigenvalue accuracy. Vector signs and ordering may vary.
Calculation source: Selected 2×2 and 3×3 eigensolvers from Math Workbench beta 0.5.