{'fraction_non_alphanumeric': 0.016835016835016835, 'fraction_numerical': 0.0, 'mean_word_length': 4.95, '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 the Solution of an Inverse Eigenvalue Problem by Newton’s Method on a Fibre Bundle with Structure Group SO(n)

In this paper a Newton-type algorithm is used to generate non-singular symmetric matrices of rank one, using a singular symmetric matrix of the same rank as an initial matrix for the iteration. In particular, numerical computations are performed with two different diagonal matrices which are in the neighbourhood of the eigenvalues of the initial singular symmetric matrix to construct a three by three and a four by four non-singular symmetric matrices to illustrate our result.