Kronecker product

Creator
Creator
Seonglae ChoSeonglae Cho
Created
Created
2024 Apr 19 12:58
Editor
Edited
Edited
2024 Oct 21 11:44
Refs
Refs
(einsum ‘ij,kl->ikjl’)
np.einsum('ij,kl->ikjl', A, B).reshape(A.shape[0] * B.shape[0], A.shape[1] * B.shape[1])

  • A product like Id⊗𝑊 (with identity on the left) represents multiplying each position in our context by a matrix.
  • A product like 𝐴⊗Id (with identity on the right) represents multiplying across positions.
  • A product like 𝐴⊗𝑊 multiplies the vector at each position by 𝑊 and across positions with 𝐴. It doesn't matter which order you do this in.
  • The products obey the mixed-product property (𝐴⊗𝐵)⋅(𝐶⊗𝐷)=(𝐴𝐶)⊗(𝐵𝐷).
 
 
 
 
 
 
 
 

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