2×2 QR Decomposition Calculator
2×2 QR Decomposition with stated conventions, validation and a worked example.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Real matrices only, at most 6 rows and 6 columns; each entry has magnitude at most 10⁹. Numerical rank uses a relative pivot threshold of 10⁻¹² after scaling by the largest entry. Near-singular matrices may be rejected or treated as lower rank. Displayed entries use 12 significant digits. Requires independent columns; R has positive diagonal.
Example Calculation
- Matrix: 3, 1; 4, 3
For [[3,1],[4,3]], Q=[[0.6,−0.8],[0.8,0.6]] and R=[[5,3],[0,1]].
Method references
Frequently asked questions
How do I use this calculator?
Enter matrix. The result updates automatically. Use Reset to restore the example values.
What method does it use?
Normalize the first column, subtract its projection from the second, and normalize the remainder: A=QR.. Real matrices only, at most 6 rows and 6 columns; each entry has magnitude at most 10⁹. Numerical rank uses a relative pivot threshold of 10⁻¹² after scaling by the largest entry. Near-singular matrices may be rejected or treated as lower rank. Displayed entries use 12 significant digits. Requires independent columns; R has positive diagonal.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.