{'fraction_non_alphanumeric': 0.011741682974559686, 'fraction_numerical': 0.0, 'mean_word_length': 5.564102564102564, '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}}
On computing multi-dimensional extreme eigen and singular subspaces

The problem, of finding extreme eigenvalues and eigenvectors of a real symmetric positive definite matrix can be viewed as a smooth optimization problem on a smooth manifold. We present a cost function approach for computing higher dimensional sub-spaces corresponding to smallest and largest eigenvalues simultaneously. This approach is then generalized to develop dynamical system for computing the singular value spread of any real matrix.