Eigenvalue Calculator
2×2 Matrix Eigenvalues
Find eigenvalues and eigenvectors of a 2×2 matrix
Eigenvalue Properties (2×2)
Check eigenvalue properties: sum equals trace, product equals determinant
Formula
det(A - λI) = 0 | 2×2: λ² - trace·λ + det = 0 | Σλᵢ = trace(A), Πλᵢ = det(A)
Frequently Asked Questions
What is an eigenvalue?
An eigenvalue λ of a matrix A satisfies Av = λv, where v is the corresponding eigenvector. This means the matrix multiplication only scales the vector, without changing its direction. Eigenvalues are found by solving det(A - λI) = 0.
How do you find eigenvalues of a 2×2 matrix?
For a 2×2 matrix [[a,b],[c,d]], solve the characteristic equation: λ² - (a+d)λ + (ad-bc) = 0. The eigenvalues are λ = [(a+d) ± √((a+d)² - 4(ad-bc))] / 2.
You may also need
+
Matrix Calculator
Free matrix calculator. Calculate the determinant, inverse, and transpose of 2×2 and 3×3 matrices.
Math+
Matrix Inverse Calculator
Free matrix inverse calculator. Find the inverse of 2x2 and 3x3 matrices with determinant check and step-by-step adjugate method.
Math+
Determinant Calculator
Free determinant calculator. Calculate the determinant of 2x2 and 3x3 matrices.
Math