The notation "V ⊗ W" represents the tensor product of two vector spaces, V and W. This operation combines the elements of both spaces to create a new vector space, which captures interactions between the vectors in V and W. The resulting space has a dimension equal to the product of the dimensions of the original spaces. In practical terms, if V has dimension m and W has dimension n, then the tensor product V ⊗ W will have dimension m × n. This concept is widely used in various fields, including physics, engineering, and computer science, to model complex systems and relationships.