are the eigenvectors of tensors. Let be a -dimensional tensor of format with entries lying in an algebraically closed field of characteristic zero. Such a tensor defines polynomial maps and with coordinates Thus each of the coordinates of is a homogeneous polynomial of degree in The eigenvectors of are the solutions of the constraint and the eigenconfiguration is given by the variety of the minors of this matrix. Other examples of tensor products Tensor product of Hilbert spaces Hilbert spaces generalize finite-dimensional vector spaces to countably-infinite dimensions. The tensor product is still defined; it is the tensor product of Hilbert spaces. Topological tensor product When the basis for a vector space is no longer countable, then the appropriate axiomatic formalization for the vector space is that of a topological vector space. The tensor product is still defined, it is the topological tensor product. Tensor product of graded vector spaces Some vector spaces can be decomposed into direct sums of subspaces. In such cases, the tensor product of two spaces can be decomposed into sums of products of the subspaces (in analogy to the way that multiplication distributes over addition). Tensor product of representations Vector spaces endowed with an additional multiplicative structure are called algebras. The tensor product of such algebras is described by the Littlewood–Richardson rule. Tensor product of quadratic forms Tensor product of multilinear forms Given two multilinear forms and on a vector space over the field their tensor product is the multilinear form This is a special case of the product of tensors if they are seen as multilinear maps (see also tensors as multilinear maps). Thus the components of the tensor product of multilinear forms can be computed by the Kronecker product. Tensor product of sheaves of modules Tensor product of line bundles Tensor product of fields Tensor product of graphs It should be mentioned that, though called "tensor product", this is not a tensor product of graphs in the above sense; actually it is the category-theoretic product in the category of graphs and graph homomorphisms. However it is actually the Kronecker tensor product of the adjacency matrices of the graphs. Compare also the section Tensor product of linear maps above. Monoidal categories The most general setting for the tensor product is the monoidal category. It captures the algebraic essence of tensoring, without making any specific reference to what is being tensored. Thus, all tensor products can