2x2 Eigenvalue Calculator
Eigenvalues of a 2x2 matrix from the characteristic equation.
Enter your values
Enter the a11 you are working with.
Enter the a12 you are working with.
Enter the a21 you are working with.
Enter the a22 you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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
At a glance
| What it does | Eigenvalues of a 2x2 matrix from the characteristic equation. |
|---|---|
| Category | Math |
| Inputs needed | A11, A12, A21, A22 |
| Main output | Eigenvalue 1 |
| Formula | λ = (tr ± sqrt(tr^2-4det))/2 |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- A11
- Enter the a11 you are working with.
- A12
- Enter the a12 you are working with.
- A21
- Enter the a21 you are working with.
- A22
- Enter the a22 you are working with.
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.
What do I need to enter into the 2x2 Eigenvalue Calculator?
Just 4 values: a11, a12, a21, a22. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the 2x2 Eigenvalue Calculator work out the answer?
Eigenvalues solve λ^2 - trace*λ + det = 0, so λ = (trace ± sqrt(trace^2-4det))/2. It applies the formula λ = (tr ± sqrt(tr^2-4det))/2 and shows the working so you can check each step by hand.
Is the 2x2 Eigenvalue Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.