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sci.matrix-eigenvalue-2x2 Calculator
Calculates the eigenvalues λ of a 2×2 matrix from the characteristic equation det(A − λI) = 0: λ = (tr ± √(tr²−4det))/2, and corresponding eigenvectors. Complex eigenvalues indicate oscillatory dynamics — a rotation matrix has eigenvalues e^(±iθ), reflecting the periodic nature of rotation.
Inputs
A11
Reference formula or conversion factor shown for context.
A12
Reference formula or conversion factor shown for context.
A21
Reference formula or conversion factor shown for context.
A22
Reference formula or conversion factor shown for context.
Results
eigenvalue λ₁
The computed numeric or monetary value.
eigenvalue λ₂
The computed numeric or monetary value.
trace = λ₁+λ₂
Reference formula or conversion factor shown for context.
det = λ₁·λ₂
Reference formula or conversion factor shown for context.
characteristic: λ²-trace·λ+det=0
Reference formula or conversion factor shown for context.
matrix type
The classification or type assigned based on the inputs.