toqito.matrices.iden

toqito.matrices.iden(dim, is_sparse=False)[source]

Calculate the dim-by-dim identity matrix [WIKID].

Returns the dim-by-dim identity matrix. If is_sparse = False then the matrix will be full. If is_sparse = True then the matrix will be sparse.

\[\begin{split}\mathbb{I} = \begin{pmatrix} 1 & 0 & 0 & \ldots & 0 \\ 0 & 1 & 0 & \ldots & 0 \\ 0 & 0 & 1 & \ldots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \ldots & 1 \end{pmatrix}\end{split}\]

Only use this function within other functions to easily get the correct identity matrix. If you always want either the full or the sparse identity matrix, just use numpy’s built-in np.identity function.

Examples

The identity matrix generated from \(d = 3\) yields the following matrix:

\[\begin{split}\mathbb{I}_3 = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}\end{split}\]
>>> from toqito.matrices import iden
>>> iden(3)
[[1., 0., 0.],
 [0., 1., 0.],
 [0., 0., 1.]])

It is also possible to create sparse identity matrices. The sparse identity matrix generated from \(d = 10\) yields the following matrix:

>>> from toqito.matrices import iden
>>> iden(10, True)
<10x10 sparse matrix of type '<class 'numpy.float64'>' with 10 stored
elements (1 diagonals) in DIAgonal format>

References

Parameters:

  • dim – Integer representing dimension of identity matrix.

  • is_sparse – Whether or not the matrix is sparse.

Returns:

Sparse identity matrix of dimension dim.