tensor product. The tensor product, outer product and Kronecker product all convey the same general idea. The differences between these are that the Kronecker product is just a tensor product of matrices, with respect to a previously-fixed basis, whereas the tensor product is usually given in its intrinsic definition. The outer product is simply the Kronecker product, limited to vectors (instead of matrices). The class of all objects with a tensor product In general, whenever one has two mathematical objects that can be combined in a way that behaves like a linear algebra tensor product, then this can be most generally understood as the internal product of a monoidal category. That is, the monoidal category captures precisely the meaning of a tensor product; it captures exactly the notion of why it is that tensor products behave the way they do. More precisely, a monoidal category is the class of all things (of a given type) that have a tensor product. Other products in linear algebra Other kinds of products in linear algebra include: Hadamard product Kronecker product The product of tensors: Wedge product or exterior product Interior product Outer product Tensor product Cartesian product In set theory, a Cartesian product is a mathematical operation which returns a set (or product set) from multiple sets. That is, for sets A and B, the Cartesian product is the set of all ordered pairs —where and . The class of all things (of a given type) that have Cartesian products is called a Cartesian category. Many of these are Cartesian closed categories. Sets are an example of such objects. Empty product The empty product on numbers and most algebraic structures has the value of 1 (the identity element of multiplication), just like the empty sum has the value of 0 (the identity element of addition). However, the concept of the empty product is more general, and requires special treatment in logic, set theory, computer programming and category theory. Products over other algebraic structures Products over other kinds of algebraic structures include: the Cartesian product of sets the direct product of groups, and also the semidirect product, knit product and wreath product the free product of groups the product of rings the product of ideals the product of topological spaces the Wick product of random variables the cap, cup, Massey and slant product in algebraic topology the smash product and wedge sum (sometimes called