Tensor product of Matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg128472] Tensor product of Matrices*From*: Sensei <sensei_s_mail_is_at at me.com>*Date*: Tue, 23 Oct 2012 00:56:17 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

Hi everyone! I've succeeded with your help in implementing a tensor application, but now I need your help on tensor products, I hope you won't mind! This is simple: I want to "add" a row and a column to a matrix. This is easy with a matrix: A = { {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {0, 0, 0} }; B = { {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0} }; M = Partition[Table[i, {i, 1, 9}], 3]; A.M.B {{1, 2, 3, 0}, {4, 5, 6, 0}, {7, 8, 9, 0}, {0, 0, 0, 0}} Now how can we do this with a tensor? This is the tensors I'm using: Id = SparseArray[ Flatten[Table[{i, j, i, j} -> 1, {i, 1, 3}, {j, 1, 3}], 1], {3, 3, 4, 4} ]; Flatten[Id, {{3}, {4}, {1, 2}}].Flatten[M, {{1, 2}}] // Normal {{1, 2, 3, 0}, {4, 5, 6, 0}, {7, 8, 9, 0}, {0, 0, 0, 0}} IIRC, I'm using Id_ijkl M_ij, but Id_ijkl = X_ki Y_jl, where this is the tensor product. How can I make this product? Wherever I search the web, I find references to the Kroneker product, which isn't what I'm looking for. Thanks!