Understand the subject
What is Schur decomposition?
Schur decomposition changes to an orthogonal basis where a supported matrix becomes especially simple.
Use it for the page’s real symmetric matrix scope.
See the structure
What the calculation is doing
A=L×UA≈QTQᵀ
Worked interpretation
Read the result in context
A≈QTQᵀ
Interpret with care
Important boundary
For this symmetric contract, T is diagonal; general real matrices need a broader Schur form.
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 ≈ QTQᵀ
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
For a symmetric matrix, T is diagonal and Q is orthogonal.
A ≈ QTQᵀ
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 bounded contract supports real symmetric matrices.
