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We consider products of matrix exponentials under the assumption that the matrices span a nilpotent Lie algebra. In 1995, Leonid Gurvits conjectured that nilpotency implies that these products are, in some sense, simple. More precisely, there exists a uniform bound l such that any product can be represented as a product of no more than l matrix exponentials. This conjecture has important applications in the analysis of linear switched systems, as it is closely related to the problem ofdoi:10.1109/tac.2007.899047 fatcat:gzzdssa3zbemjibe3qgj6acxhi