export declare function dot(a: number[], b: number[]): number;
export declare function matVecMul(A: number[][], v: number[]): number[];
export declare function outer(v1: number[], v2: number[]): number[][];
export declare function norm2(v: number[]): number;
/**
 * Returns v / ||v||, or null when ||v|| is (numerically) zero so callers
 * can handle degenerate vectors explicitly instead of propagating NaN.
 */
export declare function normalizeOrNull(v: number[]): number[] | null;
/**
 * Returns v / ||v||. Throws on a zero (or non-finite) norm rather than
 * silently producing NaN entries.
 */
export declare function normalize(v: number[]): number[];
export interface SymmetricEigenOptions {
    maxIter?: number;
    tol?: number;
    seed?: number;
}
/**
 * Computes the top-k eigenpairs of a symmetric matrix via power iteration
 * with deflation. Compared to a naive power method it adds:
 * - seeded pseudo-random initialization (deterministic, but avoids the
 *   all-ones vector stalling when (1, ..., 1) is an exact eigenvector);
 * - Gram-Schmidt re-orthogonalization against previously extracted vectors
 *   on every iteration, so components stay orthogonal even for
 *   near-degenerate spectra;
 * - a convergence criterion (vector change < tol, up to sign) with early
 *   stopping instead of a fixed iteration count;
 * - zero-norm guards: when the deflated matrix annihilates the search space
 *   the eigenvalue is reported as exactly 0 with a deterministic vector from
 *   the orthogonal complement, never NaN.
 */
export declare function symmetricEigen(A: number[][], k: number, options?: SymmetricEigenOptions): {
    values: number[];
    vectors: number[][];
};