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@arki/math/linear-algebra

Dense float64 on plain arrays (number[], number[][]): no wrapper class, so values go to JSON and other libraries as they are, and results never share memory with inputs. solve, inverse and determinant use LU with partial pivoting. A matrix singular to working precision throws SingularMatrixError (pivot at or below n·ε·‖A‖∞; { tolerance } overrides). Import it from its subpath; the root does not re-export it.

import { determinant, inverse, solve } from '@arki/math/linear-algebra';
 
solve(
  [
    [2, 1, 1],
    [4, -6, 0],
    [-2, 7, 2],
  ],
  [5, -2, 9],
); // [1, 1, 2]
determinant([
  [2, 1, 1],
  [4, -6, 0],
  [-2, 7, 2],
]); // -16
inverse([
  [1, 2],
  [3, 4],
]); // [[-2, 1], [1.5, -0.5]]

Decompositions follow LAPACK's algorithms: pivoted Householder QR, Cholesky (NotPositiveDefiniteError when it fails), SVD (Golub–Kahan–Reinsch), and eigenvalues — symmetric by Householder tridiagonalization and implicit QL, general by balancing, Hessenberg reduction and Francis double-shift QR. leastSquares uses pivoted QR and returns the minimum-norm solution when A is rank-deficient. rank counts singular values above max(m, n)·ε·σ₁ (NumPy's rule); { method: 'elimination' } uses LU instead. conditionNumber is Infinity for an exactly singular matrix, like NumPy's cond. General eigenvalues come back as Complex, sorted like polynomialRoots.

import { eigenvalues, leastSquares, singularValues, symmetricEigenvalues } from '@arki/math/linear-algebra';
 
symmetricEigenvalues([
  [2, 1],
  [1, 2],
]); // [1.0000000000000002, 3]   ascending
eigenvalues([
  [0, -1],
  [1, 0],
]).map(String); // ['-i', 'i']   a rotation
singularValues([
  [3, 0],
  [4, 5],
]); // [6.708203932499369, 2.23606797749979]
leastSquares(
  [
    [1, 1],
    [1, 2],
    [1, 3],
  ],
  [1, 2, 2],
); // [0.666…, 0.5]   intercept, slope