Use this matrix operation to transform, inspect, serialize, or decompose a rectangular numeric array with known dimensions and mathematical assumptions.

Matrix

Required list input.

Compute a thin SVD A = UΣVᵀ for a real matrix up to 20×20 with one-sided Jacobi rotations. Singular values are sorted descending; numerical precision depends on matrix conditioning. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Left singular vectors

The resulting left singular vectors returned as a list.

Singular values

The resulting singular values returned as a list.

Transposed right singular vectors

The resulting transposed right singular vectors returned as a list.

• Dimension compatibility, numeric conditioning, symmetry, positive definiteness, rank, scaling, tolerance, and floating-point precision affect matrix results. Serialization formats may lose types or precision.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Check dimensions and prerequisites, compute reconstruction or residual error for decompositions, and compare ill-conditioned cases with a trusted numerical library.

• Matrix as Table

  Convert a finite rectangular numeric matrix into canonical tool.io TableData with one Float64 field per matrix column.

• Cholesky Decomposition Calculator

  Factor a symmetric positive-definite matrix into a lower-triangular L where L times its transpose equals the input.

• LU Decomposition Calculator

  Factor a square matrix as P·A = L·U using Doolittle elimination with partial pivoting.