2x2 Eigenvalue Calculator
Eigenvalues of a 2x2 matrix from the characteristic equation.
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ⓘ Live results
Results
- Eigenvalue 1
- 5
- Eigenvalue 2
- 2
- Trace
- 7
- Determinant
- 10
Quick answer
Eigenvalues solve λ^2 - trace*λ + det = 0, so λ = (trace ± sqrt(trace^2-4det))/2.
λ = (tr ± sqrt(tr^2-4det))/2
How to use the 2x2 Eigenvalue Calculator
- 1Enter the four entries of the 2x2 matrix.
- 2The trace and determinant are computed automatically.
- 3The characteristic equation is solved for both eigenvalues, real or complex.
Worked example
Using the values the calculator loads with:
Inputs
- A114
- A121
- A212
- A223
Results
- Eigenvalue 15
- Eigenvalue 22
- Trace7
- Determinant10
Frequently asked questions
Can eigenvalues be complex?
Yes, when the discriminant tr^2-4det is negative.
What are eigenvalues used for?
They describe how a matrix stretches or rotates vectors along its eigenvectors.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.