It is well-known that every global or local Lie group is locally isomorphic to a linear group. But not every global Lie group admits a finite dimensional faithful representation, and not every local Lie group can be embedded into a global Lie group. In the paper under review, the authors announce a theorem which asserts that every global or local Lie group can be faithfully represented in the space of so-called \(\gamma\)-invertible infinite dimensional matrices. Here an infinite dimensional matrix \(A\) is said to be \(\gamma\)-invertible if both \(A\) and the transpose \(A^T\) are injective on the space of infinite dimensional vectors with finitely many nonzero entries. A detailed proof of the theorem will appear in a forthcoming paper of the same authors.