CALCULATE WITH CONFIDENCE

Linear Algebra & Matrices

Singular Value Decomposition Calculator

Compute a compact numerical SVD and disclose its rank tolerance.

Linear Algebra & Matrices

Enter matrix values

Exact structural results; labelled numerical approximations where required
Matrix A

Use signed finite decimals. Fill every visible cell. Fractions, commas, and scientific notation are not accepted.

Linear algebra result

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Enter valid values to see the result.

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Quick guide

How to use this calculator

  1. Set the matrix dimensions required by the task.
  2. Fill every visible entry and any operation-specific control.
  3. 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.