ar value decomposition of A, then :math:`A^+ = Q_2 \Sigma^+ Q_1^T`, where :math:`Q_{1,2}` are orthogonal matrices, :math:`\Sigma` is a diagonal matrix consisting of A's so-called singular values, (followed, typically, by zeros), and then :math:`\Sigma^+` is simply the diagonal matrix consisting of the reciprocals of A's singular values (again, followed by zeros). [1]_ References ---------- .. [1] G. Strang, *Linear Algebra and Its Applications*, 2nd Ed., Orlando, FL, Academic Press, Inc., 1980, pp. 139-142. Examples -------- The following example checks that ``a * a+ * a == a`` and ``a+ * a * a+ == a+``: >>> a = np.random.randn(9, 6) >>> B = np.linalg.pinv(a) >>> np.allclose(a, np.dot(a, np.dot(B, a))) True >>> np.allclose(B, np.dot(B, np.dot(a, B))) True r¿