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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 is_valid(self):
 """Test if the matrix is positive definite Hermitian. If the matrix decomposition is available, this test checks if all eigenvalues are positive. Otherwise, the test tries to calculate a Cholesky decomposition, which can be very time-consuming for large matrices. Sparse matrices are not supported. """

        # Lazy import to improve `import odl` time
        import scipy.sparse

        if scipy.sparse.isspmatrix(self.matrix):
            raise NotImplementedError('validation not supported for sparse '
                                      'matrices')
        elif self._eigval is not None:
            return np.all(np.greater(self._eigval, 0))
        else:
            try:
                np.linalg.cholesky(self.matrix)
                return np.array_equal(self.matrix, self.matrix.conj().T)
            except np.linalg.LinAlgError:
                return False