The set of all Lorentz transformations Λ in this article is denoted formula_30. This set together with matrix multiplication forms a group, in this context known as the "Lorentz group". Also, the above expression is a quadratic form of signature (3,1) on spacetime, and the group of transformations which leaves this quadratic form invariant is the indefinite orthogonal group O(3,1), a Lie group. In other words, the Lorentz group is O(3,1). As presented in this article, any Lie groups mentioned are matrix Lie groups. In this context the operation of composition amounts to matrix multiplication.