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2×2 Characteristic Polynomial Calculator — result sheet
Calculate trace, determinant, and characteristic roots for a two-by-two matrix.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: p(λ)=λ²−trace(A)λ+det(A), where trace=a+d and determinant=ad−bc.
The polynomial coefficients are derived from trace and determinant before the two roots are calculated when they are real.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Matrix a₁₁ — minimum -1000000; maximum 1000000
- Matrix a₁₂ — minimum -1000000; maximum 1000000
- Matrix a₂₁ — minimum -1000000; maximum 1000000
- Matrix a₂₂ — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Matrix a₁₁ | 1 |
| Matrix a₁₂ | 2 |
| Matrix a₂₁ | 3 |
| Matrix a₂₂ | 4 |
p(λ)=λ²−5λ−2; roots ≈ 5.372 and −0.372.
Assumptions and limits
- All matrix entries are finite real numbers within the displayed bounds.
- The matrix is two by two and real; complex roots are classified but not symbolically returned.
- Eigenvectors, conditioning, numerical stability, and larger matrices are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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