Understand the subject
What is QR decomposition?
QR writes independent columns as perpendicular directions Q followed by upper-triangular coordinates R.
Use it for orthogonalization and supported least-squares-style work.
See the structure
What the calculation is doing
A=L×UA≈QR; QᵀQ≈I
Worked interpretation
Read the result in context
A≈QR; QᵀQ≈I
Interpret with care
Important boundary
This calculator uses labelled numerical approximation and requires the stated independent-column scope.
Use the Matrix Calculator to experiment with small exact matrix operations before applying a more specialized route.
Quick guide
How to use this calculator
- Set the matrix dimensions required by the task.
- Fill every visible entry and any operation-specific control.
- Read the result type, factors, classification, and disclosed limitations.
Calculation method
Apply the stated linear-algebra contract
A ≈ QR and QᵀQ ≈ I
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
The reduced contract requires rows ≥ columns.
A ≈ QR and QᵀQ ≈ I
Supported inputs
Precision and limits
Matrix size
Input matrices are limited to 1–6 rows and columns; operation-specific square, rank, or compatibility rules still apply.
Entry precision
Enter signed finite decimals with at most 30 digits and 15 decimal places.
Numerical policy
Results use real double-precision arithmetic, a 1e-10 structural tolerance where stated, bounded iterations, and labelled approximations.
