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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.)
Square matrices are linear endomorphisms. They are isomorphic to (1,1) tensors but not any other rank of tensors.
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.)