Download your Word document
2×2 Eigenvalue and Eigenvector Calculator result sheet — free, supported by sponsors. Your download button appears in 20 seconds.
This free download is supported by sponsors — continuing in
20
Your file is generated in your browser when you choose Download — nothing is uploaded. If this calculator returns enough numeric data, the export also includes its best-fit chart alongside the readable table.
WorldCalculate result export
2×2 Eigenvalue and Eigenvector Calculator — result sheet
Find the trace, determinant, eigenvalues, and representative eigenvectors of a general real two-by-two matrix, including complex eigenvalues.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For A=[[a,b],[c,d]], tr(A)=a+d, det(A)=ad−bc, and eigenvalues solve λ²−tr(A)λ+det(A)=0; each representative eigenvector solves (A−λI)v=0.
The calculator covers general real 2×2 matrices rather than assuming symmetry. It reports the characteristic discriminant, classifies the spectrum as two real, repeated, or complex-conjugate, and supplies a nonzero eigenvector direction for each eigenvalue when the matrix has one.
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 | 4 |
| Matrix a₁₂ | 1 |
| Matrix a₂₁ | 2 |
| Matrix a₂₂ | 3 |
Trace = 7 and determinant = 10; the eigenvalues are 5 and 2 with representative eigenvectors (1,1) and (1,−2).
Assumptions and limits
- The matrix is real and two-dimensional; eigenvectors are representative directions because any nonzero scalar multiple is also valid.
- Complex values are written as a+bi when the real matrix has a complex-conjugate spectrum.
- For a repeated scalar matrix every nonzero vector is an eigenvector, so two coordinate-basis directions are shown.
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.
No saved result was found. Please run the calculation first, then choose Download again.