Find eigenvalues and eigenvectors of 2×2 and 3×3 matrices with full step-by-step solutions including the characteristic polynomial and verification.
Fill in the matrix entries — supports decimals and negative numbers
Preset Examples
Definition
A·v = λ·v
λ is an eigenvalue, v is the corresponding eigenvector (non-zero).
Characteristic Equation
det(A − λI) = 0
Solving this polynomial gives the eigenvalues of A.
Properties
tr(A) = Σλᵢ det(A) = Πλᵢ
Trace equals sum and determinant equals product of all eigenvalues.