class_docstr: Class for the space of complex matrices (m, n).
  
  Parameters
  ----------
  m, n : int
      Integers representing the shapes of the matrices: m x n.
docstr: Compute Frobenius inner-product of two matrices.
  
  The `einsum` function is used to avoid computing a matrix product. It
  is also faster than using a sum an element-wise product.
  
  Parameters
  ----------
  mat_1 : array-like, shape=[..., m, n]
      Matrix.
  mat_2 : array-like, shape=[..., m, n]
      Matrix.
  
  Returns
  -------
  product : array-like, shape=[...,]
      Frobenius inner-product of mat_1 and mat_2
docstr_tok: ["Compute","Frobenius","inner-product","of","two","matrices",".","The","`","einsum","`","function","is","used","to","avoid","computing","a","matrix","product",".","It","is","also","faster","than","using","a","sum","an","element-wise","product",".","Parameters","--","--","--","--","--","mat_1",":","array-like",",","shape=","[","...",",","m",",","n","]","Matrix",".","mat_2",":","array-like",",","shape=","[","...",",","m",",","n","]","Matrix",".","Returns","--","--","--","-","product",":","array-like",",","shape=","[","...",",","]","Frobenius","inner-product","of","mat_1","and","mat_2"]
code: def frobenius_product(mat_1, mat_2):
      """Compute Frobenius inner-product of two matrices.
  
      The `einsum` function is used to avoid computing a matrix product. It
      is also faster than using a sum an element-wise product.
  
      Parameters
      ----------
      mat_1 : array-like, shape=[..., m, n]
          Matrix.
      mat_2 : array-like, shape=[..., m, n]
          Matrix.
  
      Returns
      -------
      product : array-like, shape=[...,]
          Frobenius inner-product of mat_1 and mat_2
      """
      return gs.einsum("...ij,...ij->...", gs.conj(mat_1), mat_2)
  
imports: import geomstats.backend
  import geomstats.errors
  from geomstats.geometry.base import ComplexMatrixVectorSpace
  from geomstats.geometry.hermitian import HermitianMetric
  from geomstats.geometry.matrices import Matrices
  from geomstats.vectorization import repeat_out
label_desc: Use image node_id 12 for calling the ComplexMatrices obj's underlying member method code with example usage: obj.frobenius_product(mat_1, mat_2) and returns: gs