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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def ishermitian(A, fast_check=True, tol=1e-6, verbose=False):
 r"""Return True if A is Hermitian to within tol. Parameters A : {dense or sparse matrix} fast_check : {bool} If True, use the heuristic < Ax, y> = < x, Ay> for random vectors x and y to check for conjugate symmetry. If False, compute A - A.H. tol : {float} Symmetry tolerance verbose: {bool} prints max( \|A - A.H\| ) if nonhermitian and fast_check=False abs( <Ax, y> - <x, Ay> ) if nonhermitian and fast_check=False Returns ------- True if hermitian False if nonhermitian Notes ----- This function applies a simple test of conjugate symmetry Examples -------- False True """

    # convert to matrix type
    if not sparse.isspmatrix(A):
        A = np.asmatrix(A)

    if fast_check:
        x = sp.rand(A.shape[0], 1)
        y = sp.rand(A.shape[0], 1)
        if A.dtype == complex:
            x = x + 1.0j*sp.rand(A.shape[0], 1)
            y = y + 1.0j*sp.rand(A.shape[0], 1)
        xAy = np.dot((A*x).conjugate().T, y)
        xAty = np.dot(x.conjugate().T, A*y)
        diff = float(np.abs(xAy - xAty) / np.sqrt(np.abs(xAy*xAty)))

    else:
        # compute the difference, A - A.H
        if sparse.isspmatrix(A):
            diff = np.ravel((A - A.H).data)
        else:
            diff = np.ravel(A - A.H)

        if np.max(diff.shape) == 0:
            diff = 0
        else:
            diff = np.max(np.abs(diff))

    if diff < tol:
        diff = 0
        return True
    else:
        if verbose:
            print(diff)
        return False

    return diff