Eigenvalues are scale factors for directions that a matrix does not rotate away from themselves.
Eigenvalue Calculator
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Your eigenvalues are:
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Table of Contents
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What is Eigenvalue?
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How to Use This Calculator
- Enter or select a1, a2, b1, b2.
- Check the unit beside each measurement. For a percentage or rate, use the scale and time period stated in the form.
- Choose Calculate, then compare the output with the formula and example below. If you change a value or option, calculate again to update the result.
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Formula Used
For a 2 × 2 matrix: λ² − trace(A)λ + det(A) = 0
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Variables Explained
| Input | What it means |
|---|---|
| a1 | A value or coefficient in the formula above; keep the displayed position and sign. |
| a2 | A value or coefficient in the formula above; keep the displayed position and sign. |
| b1 | A value or coefficient in the formula above; keep the displayed position and sign. |
| b2 | A value or coefficient in the formula above; keep the displayed position and sign. |
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Worked Example
For [[2,0],[0,3]], the eigenvalues are 2 and 3.
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Why Use This Calculator?
Identify the scale factors that govern repeated application of a matrix.
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Common Mistakes
- A negative discriminant gives complex eigenvalues even when every matrix entry is real.
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Frequently Asked Questions
Should I round numbers before calculating?
Keep the original input precision through the calculation and round the final answer to the precision you need. Rounding an intermediate result can change later steps.
Why can a manual calculation differ slightly?
Check the operation, units, signs and rounding first. Equivalent fractions or expressions can look different while representing the same value.
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Sources & References
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