Eigenvalue and Eigenvector Calculator
Result
Eigenvalue and Eigenvector Calculator (2×2) The Eigenvalue and Eigenvector Calculator finds the eigenvalues and eigenvectors of a 2×2 matrix by solving its characteristic equation. Enter the four matrix entries. — free online calculator.
Formula
- Eigenvalue and Eigenvector Calculator calculates its result from a11, a12, a21, a22. It uses the formula Eigenvalues solve λ² − tr(A)λ + det(A)=0; eigenvectors solve (A−λI)v=0.. Change any input to recalculate the result instantly.
- The main inputs are a11, a12, a21, a22. Enter them in the units and format shown in the calculator.
- Keep comparable quantities in compatible units whenever the formula combines or compares them.
- Changing any input above recalculates the result with the same calculation engine used by this page.
Example: Eigenvalue and Eigenvector
- a11: 2
- a12: 1
- a21: 1
- a22: 2
Using a11 = 2, a12 = 1, a21 = 1, a22 = 2, the calculated result is λ1: 3 | v1: [1, 1] | λ2: 1 | v2: [1, -1].
Sample result: Calculating…
Frequently asked questions
What does the Eigenvalue and Eigenvector calculate?
Eigenvalue and Eigenvector Calculator (2×2) The Eigenvalue and Eigenvector Calculator finds the eigenvalues and eigenvectors of a 2×2 matrix by solving its characteristic equation. Enter the four matrix entries. — free online calculator.
Which values should I enter?
Enter a11, a12, a21, a22 using the units and format shown beside each field.
What formula does this calculator use?
The calculator uses the following relationship: Eigenvalues solve λ² − tr(A)λ + det(A)=0; eigenvectors solve (A−λI)v=0..
Why might my result differ from another source?
Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.
Does the result update automatically?
Yes. Changing an input updates the result using the same calculation engine shown on this page.