/**
 * Dense linear-algebra kernels used by the discriminant-analysis estimators.
 *
 * Both routines are Jacobi methods: slower than LAPACK-style algorithms but
 * unconditionally convergent, fully deterministic, and accurate to machine
 * precision for the small/medium matrices this library targets. Unlike the
 * top-k power iteration in `src/algebra/eigen.ts` they return the FULL
 * spectrum, which the sklearn-style tol-based rank cutting requires.
 */
/**
 * Thin singular value decomposition (values + right singular vectors) of an
 * n x p matrix via one-sided (Hestenes) Jacobi rotations.
 *
 * Returns `S` (length min(n, p), descending, all >= 0) and `Vt`
 * (min(n, p) x p, orthonormal rows) such that A ~= U diag(S) Vt. The left
 * singular vectors are not materialized because no caller needs them.
 */
export declare function jacobiSVD(A: number[][]): {
    S: number[];
    Vt: number[][];
};
/**
 * Full eigendecomposition of a symmetric matrix via the classical two-sided
 * Jacobi eigenvalue algorithm. Returns all eigenpairs sorted by eigenvalue
 * descending; `vectors[i]` is the (unit-norm) eigenvector for `values[i]`.
 */
export declare function symmetricEigDecomposition(A: number[][]): {
    values: number[];
    vectors: number[][];
};
/**
 * Cholesky factorization A = L L^T for a symmetric positive-definite matrix.
 * Returns the lower-triangular factor, or null when A is not (numerically)
 * positive definite so callers can raise a domain-specific error.
 */
export declare function cholesky(A: number[][]): number[][] | null;
/** Solve L x = b for lower-triangular L (forward substitution). */
export declare function solveLower(L: number[][], b: number[]): number[];
/** Solve L^T x = b for lower-triangular L (backward substitution). */
export declare function solveLowerTransposed(L: number[][], b: number[]): number[];