import { MatN } from '../math/matn.js';
export interface SymmetricEigenOptions {
    /** Relative convergence threshold for the off-diagonal Frobenius norm. */
    tolerance?: number;
    /** Relative tolerance used to validate that the input is symmetric. */
    symmetryTolerance?: number;
    /** Maximum number of complete cyclic Jacobi sweeps. */
    maxSweeps?: number;
}
export interface SymmetricEigensystem {
    /** Eigenvalues in ascending order. */
    readonly values: Float64Array;
    /** Orthonormal eigenvectors stored as columns. */
    readonly vectors: MatN;
    /** Absolute Euclidean residual ||A v_i - lambda_i v_i|| for each pair. */
    readonly residualNorms: Float64Array;
    readonly sweeps: number;
    readonly rotations: number;
    readonly maxResidual: number;
    /** Max absolute entry of V^T V - I. */
    readonly orthogonalityError: number;
}
/**
 * Deterministic Float64 eigendecomposition of a real symmetric matrix.
 *
 * A cyclic Jacobi iteration is used as the auditable dense reference path.
 * It is intentionally not a sparse large-matrix solver. Equal and nearly
 * equal eigenvalues define an invariant eigenspace, but the individual basis
 * vectors returned inside that space are not mathematically unique.
 */
export declare function symmetricEigenDecomposition(matrix: MatN, options?: SymmetricEigenOptions): SymmetricEigensystem;
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