A tensor product is a mathematical operation that combines two vector spaces to create a new vector space. This new space captures the interactions between the original spaces, allowing for the representation of more complex relationships. Tensor products are commonly used in various fields, including physics and engineering, to describe multi-dimensional data. In more technical terms, if you have two vector spaces, V and W, their tensor product, denoted as V ⊗ W, consists of all possible linear combinations of pairs of vectors from V and W. This operation is essential in areas like quantum mechanics and machine learning, where multi-dimensional structures are analyzed.