/** Options for {@link orth}. */
export interface OrthOptions {
    /**
     * Rank-determination tolerance. Singular values `> tol` count toward the
     * rank. Default: `max(m, n) * S[0] * 2.22e-16` (machine epsilon scaled by
     * matrix size and the largest singular value).
     */
    tol?: number;
}
/**
 * Orthonormal basis for the column space of `A`.
 *
 * Computes `{ U, S } = svd(A)` and returns the first `r` columns of `U`,
 * where `r` is the number of singular values above `tol`. For the all-zero
 * matrix (`r = 0`), returns an `m x 0` matrix (each row an empty array).
 *
 * @example
 * orth([[1,0,1],[0,1,1],[1,1,2]])  // rank 2 -> 3x2 matrix, U^T U = I
 */
export declare function orth(A: number[][], opts?: OrthOptions): number[][];
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