Birkhoff decompositions and Iwasawa decompositions for loop groups
Birkhoff decompositions and Iwasawa decompositions for loop groups
Representations of arbitrary real or complex invertible matrices as products of matrices of special type have been used for many purposes. The matrix form of the Gram-Schmidt orthonormalization procedure and the Gauss elimination process are instances of such matrix factorizations. For arbitrary, finite-dimensional, semisimple Lie groups, the corresponding matrix factorizations …