For bounded matrices , the Lie product formula gives operator norm convergenceFor two summands, expanding their matrix exponentials gives the one-step difference below. For Hermitian matrices multiplied by , the factors are unitary operators and the first-order unitary product-formula error bound gives an explicit error estimate.
The Lie product formula, also known as the Baker-Campbell-Hausdorff formula (BCH formula), describes the relationship between the exponential of Lie algebras and the products of elements in the algebra. It provides a way to express the product of two exponentials of elements from a Lie algebra in terms of their commutators.
New to topics? Read the docs here!