Frequently Asked Questions
What is an eigenvalue?
A scalar λ such that A·v = λ·v for some nonzero vector v. It is how much the matrix scales vectors that lie along its eigenvector direction.
Is the eigenvector unique?
Only up to nonzero scaling. Any constant multiple of an eigenvector is still an eigenvector. The calculator returns the unit-length version.
Why does my 3x3 matrix have complex eigenvalues?
Real matrices can have complex conjugate pairs of eigenvalues when they include a rotation. This usually means the matrix is not diagonalizable over the reals.
How do you find the eigenvalues of a 2x2 matrix?
Solve the characteristic equation λ² − tr(A)·λ + det(A) = 0, where tr(A) is the trace (sum of the diagonal) and det(A) is the determinant. The two roots are the eigenvalues.
What is the characteristic polynomial?
It is det(A − λI), a polynomial in λ whose roots are exactly the eigenvalues of the matrix. For an n×n matrix it has degree n, so there are n eigenvalues counted with multiplicity.
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Important Disclaimer: Estimates for informational purposes only.
This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.