{'fraction_non_alphanumeric': 0.02529182879377432, 'fraction_numerical': 0.0, 'mean_word_length': 4.8522727272727275, '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}}
Normality conditions for the BHH matrix operator

The matrix operator defined by the left-hand side of the Bevis–Hall–Hartwig equation(briefly, the BHH operator) is not linear in the space of complex matrices . However, it becomes a linear operator if every matrix is replaced by the pair of real matrices of the same size, namely, by its real and imaginary parts. Introducing an appropriate scalar product in the resulting real space, we find necessary and sufficient conditions for the BHH operator to be normal.