⚡ Eigenvalue & Eigenvector

2×2 & 3×3 · step-by-step · diagonalization · visualization
Enter matrix and click Compute.

❓ Frequently Asked Questions

What if eigenvalues are complex?
The calculator displays complex eigenvalues in a+bi form. Eigenvectors for complex eigenvalues are shown but not visualized.
How is the characteristic polynomial computed?
For 2x2: λ² − tr(A)λ + det(A). For 3x3: cofactor expansion yields cubic; roots via Durand‑Kerner (simplified).
Is diagonalization always possible?
If eigenvectors form a basis (geometric multiplicity = algebraic), we show P, D, P⁻¹ and verify.

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