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Characteristic Polynomial Calculator

Characteristic polynomial calculator helps you determine the characteristic polynomial of any matrix of size 2×2, 3×3, or 4×4.

One row per line, values separated by commas or spaces.
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Eigenvalues8.87298335, 1.12701665all real
Trace10equals the sum of the eigenvalues
Determinant10equals the product of the eigenvalues
Rank2
Sum of eigenvalues10
Product of eigenvalues10

Your matrix

47
26

The method

solve det(A − λI) = 0 for the eigenvalues λ

What an eigenvalue is

An eigenvector is a direction the matrix does not turn — it only stretches it. The eigenvalue is how much: Av = λv. Complex eigenvalues mean no real direction survives unturned, which is the signature of a rotation.

Two useful checks: the eigenvalues always sum to the trace and multiply to the determinant. Both are shown above.