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

.. py:module:: ulab.linalg

.. autoapi-nested-parse::

   Linear algebra functions





.. function:: cholesky(A)

   :param ~ulab.array A: a positive definite, symmetric square matrix
   :return ~ulab.array 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*


.. function:: det()

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


.. function:: dot(m1, m2)

   :param ~ulab.array m1: a matrix, or a vector
   :param ~ulab.array m2: a matrix, or a vector

   Computes the product of two matrices, or two vectors. In the letter case, the inner product is returned.


.. function:: eig(m)

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

   Computes the eigenvalues and eigenvectors of a square matrix


.. function:: inv(m)

   :param ~ulab.array 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


.. function:: norm(x: ulab.array) -> float

   :param ~ulab.array 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.


.. function:: size(array)

   Return the total number of elements in the array, as an integer.


.. function:: trace(m)

   :param m: a square matrix

   Compute the trace of the matrix, the sum of its diagonal elements.