2×2 Characteristic Polynomial Calculator
Result
2×2 Characteristic Polynomial Calculator — dedicated 2×2 method with domain checks.
Formula
- 2×2 Characteristic Polynomial Calculator. For A = [[a11,a12],[a21,a22]], tr(A) = a11 + a22 and det(A) = a11a22 − a12a21. Its characteristic polynomial is p(λ) = det(λI−A) = λ² − tr(A)λ + det(A). The calculator reports an explicit result within this documented 2×2 scope.
- 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: 2×2 Characteristic Polynomial
- a11: 1
- a12: 2
- a21: 3
- a22: 4
For [[1,2],[3,4]], trace = 5, determinant = −2, and p(λ) = λ² − 5λ − 2.
Sample result: Calculating…
Frequently asked questions
What does the 2×2 Characteristic Polynomial calculate?
2×2 Characteristic Polynomial Calculator — dedicated 2×2 method with domain checks.
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: For A = [[a11,a12],[a21,a22]], tr(A) = a11 + a22 and det(A) = a11a22 − a12a21. Its characteristic polynomial is p(λ) = det(λI−A) = λ² − tr(A)λ + det(A)..
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.