matrix_ops.calculate_vector_matrix_dimension¶

Calculates the (common) dimension of a set of vectors or matrices.

Functions¶

calculate_vector_matrix_dimension(item)

Calculate the dimension of a vector or a square matrix, including 2D representations of vectors.

Module Contents¶

matrix_ops.calculate_vector_matrix_dimension.calculate_vector_matrix_dimension(item)¶

Calculate the dimension of a vector or a square matrix, including 2D representations of vectors.

This function determines the dimension of the provided item, treating 1D arrays as vectors, 2D arrays with one dimension being 1 as vector representations, and square 2D arrays as density matrices. The dimension is the length for vectors and the square of the side length for density matrices.

Parameters:: item (numpy.ndarray) – The item whose dimension is being calculated. Can be a 1D array (vector), a 2D array representing a vector with one dimension being 1, or a square 2D array (density matrix).
Returns:: int The dimension of the item. For vectors (1D or 2D representations), it’s the length. For square matrices, it’s the square of the size of one side.
Raises:: ValueError – If the input is not a numpy array, not a 1D array (vector), a 2D array representing a vector, or a square 2D array (density matrix).
Returns:: The dimension of the vector or matrix.
Return type:: int

Example:¶

Consider the following three-dimensional vector:

\[v = \left[ 1, 0, 0 \right]^{\text{T}}.\]

For this case, the dimension of the vector is equal to its length

>>> from toqito.matrix_ops import calculate_vector_matrix_dimension
>>> import numpy as np
>>> v = np.array([1, 0, 0])
>>> calculate_vector_matrix_dimension(v)
3

For the density matrix of some two-dimensional quantum system

\[\begin{split}\rho = \frac{1}{2} \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\end{split}\]

>>> from toqito.matrix_ops import calculate_vector_matrix_dimension
>>> import numpy as np
>>> rho = np.array([[1/2, 0],[0, 1/2]])
>>> calculate_vector_matrix_dimension(rho)
2