:mod:`ulab.numpy.linalg`
========================

.. py:module:: ulab.numpy.linalg





.. py:function:: cholesky(A: ulab.numpy.ndarray) -> ulab.numpy.ndarray

   :param ~ulab.numpy.ndarray A: a positive definite, symmetric square matrix
   :return ~ulab.numpy.ndarray L: a square root matrix in the lower triangular form
   :raises ValueError: If the input does not fulfill the necessary conditions

   The returned matrix satisfies the equation m=LL*


.. py:function:: det(m: ulab.numpy.ndarray) -> float

   :param: m, a square matrix
   :return float: The determinant of the matrix

   Computes the eigenvalues and eigenvectors of a square matrix


.. py:function:: eig(m: ulab.numpy.ndarray) -> Tuple[ulab.numpy.ndarray, ulab.numpy.ndarray]

   :param m: a square matrix
   :return tuple (eigenvectors, eigenvalues):

   Computes the eigenvalues and eigenvectors of a square matrix


.. py:function:: inv(m: ulab.numpy.ndarray) -> ulab.numpy.ndarray

   :param ~ulab.numpy.ndarray m: a square matrix
   :return: The inverse of the matrix, if it exists
   :raises ValueError: if the matrix is not invertible

   Computes the inverse of a square matrix


.. py:function:: norm(x: ulab.numpy.ndarray) -> float

   :param ~ulab.numpy.ndarray x: a vector or a matrix

   Computes the 2-norm of a vector or a matrix, i.e., ``sqrt(sum(x*x))``, however, without the RAM overhead.


.. py:function:: qr(m: ulab.numpy.ndarray) -> Tuple[ulab.numpy.ndarray, ulab.numpy.ndarray]

   :param m: a matrix
   :return tuple (Q, R):

   Factor the matrix a as QR, where Q is orthonormal and R is upper-triangular.