Introduction to Mathematical Logic, Sixth Edition
《Introduction to Mathematical Logic, Sixth Edition》 · 第 538–539 页 · Chapter 11，Section 11.6「Gauss Decomposition」
The final structural result that we need for Chapter 12 is the Gauss decomposition of $G$ relative to a diagonal torus $A subset G$ (the factorization of a matrix as a product of a block upper-triangular unipotent matrix, a block-diagonal matrix, and a block lower-triangular unipotent matrix, with the block sizes determined by the multiplicities of the weights of $A$).