Characteristic Polynomial Calculator (2×2)

Math

The Characteristic Polynomial Calculator finds the characteristic polynomial λ² − (trace)λ + det of a 2×2 matrix, whose roots are the eigenvalues. Enter the four entries.

Formula

p(λ) = λ² − (trace)·λ + det = λ² − (a₁₁+a₂₂)λ + (a₁₁a₂₂ − a₁₂a₂₁)
  • The roots of the characteristic polynomial are the matrix's eigenvalues.
  • Trace = a₁₁ + a₂₂; determinant = a₁₁a₂₂ − a₁₂a₂₁.

[[2,1],[1,2]]

Inputs
  • a₁₁: 2
  • a₁₂: 1
  • a₂₁: 1
  • a₂₂: 2

trace 4, det 3 → λ² − 4λ + 3, with roots 1 and 3.

Frequently asked questions

What is the characteristic polynomial?
It is det(A − λI). Its roots are the eigenvalues of the matrix.