code: def product_homomorphism(*elements):
      """
      Given a sequence of elements of the same subclass of MatrixGroup,
      they can be thought of as an element of the topological product,
      which has a natural group structure.
  
      If all of the elements are of the same subclass, then there is a
      natural group homomorphism from the product space to a larger
      MatrixGroup. The matrices of the elements of the larger group will
      be block diagonal with blocks of the size corresponding to the
      dimensions of each corresponding element.
  
      This function is that homomorphism.
      """
      type_e0 = type(elements[0])
      notsame = [e for e in elements if type(e) != type_e0]
      if notsame:
          raise ValueError(
              "all elements should be members of the same group"
          )
  
      newcmap = cmap_product(*elements)
      matrix = newcmap.affine[:-1, :-1]
      return elements[0].__class__(matrix, newcmap.function_domain)
  
imports: import numpy
  from nipy.core.api import AffineTransform, CoordinateSystem
  from nipy.core.reference.coordinate_map import compose
  from nipy.core.reference.coordinate_map import product
label_desc: Use image node_id 4 for calling a global function with example usage: product_homomorphism() and returns: elements