toqito.matrices.gen_gell_mann
=============================

.. py:module:: toqito.matrices.gen_gell_mann

.. autoapi-nested-parse::

   Produces the generalized Gell-Mann operator matrices.





Module Contents
---------------

.. py:function:: gen_gell_mann(ind_1, ind_2, dim)

   Produce a generalized Gell-Mann operator [@WikiGellMann].

   Construct a `dim`-by-`dim` Hermitian operator. These matrices
   span the entire space of `dim`-by-`dim` matrices as
   `ind_1` and `ind_2` range from 0 to `dim-1`, inclusive,
   and they generalize the Pauli operators when `dim = 2` and the
   Gell-Mann operators when `dim = 3`.

   .. rubric:: Examples

   The generalized Gell-Mann matrix for `ind_1 = 0`, `ind_2 = 1`
   and `dim = 2` is given as

   \[
       G_{0, 1, 2} = \begin{pmatrix}
                        0 & 1 \\
                        1 & 0
                     \end{pmatrix}.
   \]

   This can be obtained in `|toqito⟩` as follows.

   ```python exec="1" source="above"
   from toqito.matrices import gen_gell_mann

   print(gen_gell_mann(ind_1=0, ind_2=1, dim=2))
   ```

   The generalized Gell-Mann matrix `ind_1 = 2`, `ind_2 = 3`, and
   `dim = 4` is given as

   \[
       G_{2, 3, 4} = \begin{pmatrix}
                       0 & 0 & 0 & 0 \\
                       0 & 0 & 0 & 0 \\
                       0 & 0 & 0 & 1 \\
                       0 & 0 & 1 & 0
                     \end{pmatrix}.
   \]

   This can be obtained in `|toqito⟩` as follows.

   ```python exec="1" source="above"
   from toqito.matrices import gen_gell_mann

   gen_gell_mann(ind_1=2, ind_2=3, dim=4)
   ```

   :param ind_1: A non-negative integer from 0 to `dim-1` (inclusive).
   :param ind_2: A non-negative integer from 0 to `dim-1` (inclusive).
   :param dim: The dimension of the Gell-Mann operator.

   :returns: The generalized Gell-Mann operator as an array.