Understand the subject
What are singular values?
Singular values are non-negative stretch amounts of a matrix along specially chosen perpendicular directions.
Use them to inspect rank, scale, and sensitivity without requesting full singular vectors.
See the structure
What the calculation is doing
v→Av = λvsame direction, scaled length
Worked interpretation
Read the result in context
σᵢ=√λᵢ(AᵀA)
Interpret with care
Important boundary
Numerically tiny values are tolerance-dependent rather than exact structural zeroes.
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
σᵢ = √λᵢ(AᵀA)
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
Near-zero singular values are judged against the displayed tolerance.
σᵢ = √λᵢ(AᵀA)
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.
