Comment on Tensors
tatterdemalion@programming.dev 3 weeks ago
Matrices are linear endomorphisms. They are isomorphic to (1,1) tensors, but not any other rank of tensors.
Comment on Tensors
tatterdemalion@programming.dev 3 weeks ago
Matrices are linear endomorphisms. They are isomorphic to (1,1) tensors, but not any other rank of tensors.
affiliate@lemmy.world 3 weeks ago
a tensor is a multi-linear map V × … × V × V^^ × … × V^^ → F, and a multi-linear map V × … × V × V^^ × … × V^^ → F is the same as a linear map V ⊗ … ⊗ V ⊗ V^^ ⊗ … ⊗ V^^ → F. and a linear map is ““the same thing as”” a matrix. so in this way, you can associate matrices to tensors. (but the matrices are formed in the tensor space V ⊗ … ⊗ V ⊗ V^^ ⊗ … ⊗ V^^, not in the vector space V.)