Matrix Eigenvalue Calculator

Use our free matrix eigenvalue calculator to compute the eigenvalues of 2×2 and 3×3 matrices via the characteristic polynomial, with trace, determinant, and polynomial display.

Math

Matrix (2×2 or 3×3)

Formula

Eigenvalues λ satisfy the characteristic equation det(A − λI) = 0. For 2×2: λ² − tr(A)λ + det(A) = 0. For 3×3: λ³ − tr(A)λ² + (sum of principal minors)λ − det(A) = 0.

det(A − λI) = 0

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter a 2×2 or 3×3 square matrix.
2Click Calculate to find real eigenvalues.

Examples

2×2: [[4,1],[2,3]]

1.λ² − 7λ + 10 = 0
2.λ = 5, 2

Result: 5, 2

2×2: [[2,0],[0,3]]

1.Diagonal matrix — eigenvalues on diagonal
2.λ = 2, 3

Result: 2, 3

Frequently Asked Questions

Scalars λ such that Av = λv for some non-zero vector v.

λ² − tr(A)λ + det(A) = 0.

Occur when the discriminant is negative (not shown).

det(A − λI) = 0.

Yes, this calculator shows only real eigenvalues.

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CalculateMe Team

Last updated: 2026-07-14

Matrix Eigenvalue Calculator

Formula

How It Works

Examples

2×2: [[4,1],[2,3]]

2×2: [[2,0],[0,3]]

Frequently Asked Questions

What are eigenvalues?

2×2 formula?

What are complex eigenvalues?

What is the characteristic polynomial?

Only real eigenvalues?

Related Calculators

Matrix Eigenvalue Calculator

Formula

How It Works

Examples

2×2: [[4,1],[2,3]]

2×2: [[2,0],[0,3]]

Frequently Asked Questions

What are eigenvalues?

2×2 formula?

What are complex eigenvalues?

What is the characteristic polynomial?

Only real eigenvalues?

Related Calculators