Understand the subject
What is singular value decomposition?
SVD describes a matrix as a rotation or reflection, independent perpendicular stretches, then another rotation or reflection.
Use it to inspect rank, dominant directions, and stable low-rank structure.
See the structure
What the calculation is doing
v→Av = λvsame direction, scaled length
Worked interpretation
Read the result in context
A≈UΣVᵀ
Interpret with care
Important boundary
The result is numerical; small singular values are judged with the displayed tolerance.
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 ≈ UΣVᵀ
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
The diagonal of Σ contains retained positive singular values in descending order.
A ≈ UΣVᵀ
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.
