2 by 2 Singular Values Calculator
Calculate singular values, Frobenius norm and spectral condition number of a real 2×2 matrix.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Scale entries before forming the Gram matrix and recover the smaller singular value using the determinant.
σ1,2=√eigenvalues(AᵀA); σ2=|det A|/σ1 when σ1>0
Worked example
Diagonal entries3 and4 have singular values4 and3 and Frobenius norm5.
Assumptions and input details
Real matrix only; reports singular values, not full U/V factor matrices. Condition number is undefined for a numerically zero smaller singular value; extreme determinant cancellation can reduce relative accuracy.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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