{'fraction_non_alphanumeric': 0.027348394768133173, 'fraction_numerical': 0.0, 'mean_word_length': 5.101449275362318, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A simple solution to the optimal eigenvalue assignment problem

The problem of the optimal eigenvalue assignment for multi-input linear systems is considered. It is proven that for an n-order system with m independent inputs, the problem is split into the following two sequential stages. Initially, the n-m eigenvalues are assigned using an (n-m)-order system. This assignment is not constrained to satisfy optimality criteria. Next, an m-order system is used to assign the remaining m eigenvalues in such a way that linear quadratic optimal criteria are simultaneously satisfied. Therefore, the original n-order optimal eigenvalue assignment problem is reduced to an m-order optimal assignment problem. Moreover, the structure of the equivalent m-order system permits further simplifications which lead to solutions obtained by inspection.