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.)