Understand the subject
What is polar decomposition?
Polar decomposition separates a transformation into an orthogonal turn/flip and a positive stretching component.
Use it to distinguish orientation from stretch in a supported nonsingular square matrix.
See the structure
What the calculation is doing
A=L×UA≈QH
Worked interpretation
Read the result in context
A≈QH
Interpret with care
Important boundary
The calculator’s bounded contract does not cover every possible singular or rectangular case.
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 ≈ QH
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
For a nonsingular square matrix, Q is orthogonal and H is positive definite.
A ≈ QH
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.
Supported scope
This contract supports real nonsingular square matrices.
