A solution method for a linear system with its matrix formed as the tensor product of several matrices is presented. The algorithm works with the LU decompositions of the small matrices in the tensor product, resulting in a very efficient approach, as detailed in the complexity analysis provided.

Starting with the algebraic properties of the tensor product, the development progresses in a clear and concise manner with a figure illustrating the matrix structure at a critical part of description and pseudocode giving further details. A brief mention of some situations where tensor product matrices occur, along with references for readers interested in more detail, motivates the presentation. While somewhat specialized, this material should be of interest to researchers working in computational linear algebra, as well as those with an interest in the particular matrix structure studied.