Eigenvalue Calculator

Calculate eigenvalues and eigenvectors of 2x2 matrices. Visualize the transformation.

Enter 2x2 Matrix

Linear Transformation Visualization

OriginalTransformed

Arrows show eigenvectors (directions preserved under transformation)

Eigenvalues

Real

3.0000

Eigenvalue 1 (λ1)

2.0000

Eigenvalue 2 (λ2)

Eigenvectors

[0.0000, 1.0000]

Eigenvector 1 (v1)

[-0.7071, 0.7071]

Eigenvector 2 (v2)

Matrix Properties

5.0000

Trace (a + d)

6.0000

Determinant (ad - bc)

1.0000

Discriminant

Characteristic Polynomial

λ² - 5λ + 6 = 0

Eigenvalues are the roots of this polynomial

det(A - λI) = 0

For 2x2: λ² - (a+d)λ + (ad-bc) = 0

λ = (trace ± √(trace² - 4det)) / 2

(A - λI)v = 0 for eigenvector v

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