2D Gram–Schmidt Calculator
2D Gram–Schmidt 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.
- Two real, numerically independent 2D vectors. Threshold 10⁻¹² relative to the largest entry.
Example Calculation
- u x: 3
- u y: 4
- v x: 1
- v y: 3
u=(3,4), v=(1,3) produce q₁=(0.6,0.8), q₂=(−0.8,0.6).
Method references
Frequently asked questions
How do I use this calculator?
Enter u x, u y, v x, v y. The result updates automatically. Use Reset to restore the example values.
What method does it use?
q₁=u/||u||; q₂=(v−(q₁·v)q₁)/||v−(q₁·v)q₁||. Two real, numerically independent 2D vectors. Threshold 10⁻¹² relative to the largest entry.
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.