  Many of today's problems require techniques that involve the solution of
arbitrarily large systems $A\mathbf{x}=\mathbf{b}$. A popular numerical
approach is the so-called Greedy Rank-One Update Algorithm, based on a
particular tensor decomposition. The numerical experiments support the fact
that this algorithm converges especially fast when the matrix of the linear
system is Laplacian-Like. These matrices that follow the tensor structure of
the Laplacian operator are formed by sums of Kronecker product of matrices
following a particular pattern. Moreover, this set of matrices is not only a
linear subspace it is a a Lie sub-algebra of a matrix Lie Algebra. In this
paper, we characterize and give the main properties of this particular class of
matrices. Moreover, the above results allow us to propose an algorithm to
explicitly compute the orthogonal projection onto this subspace of a given
square matrix $A \in \mathbb{R}^{N\times N}.$
