Inverse and Moore–Penrose inverse of conditional matrices via convolution

• Published in: Journal of applied mathematics & computing Vol. 70; no. 1; pp. 417 - 433
• Main Authors: Köme, Cahit, Yazlik, Yasin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2024; Springer Nature B.V
• Subjects: Analytical techniques; Computational Mathematics and Numerical Analysis; Convolution; Inverse matrices; Linear equations; Machine learning; Mathematical and Computational Engineering; Mathematics; Mathematics and Statistics; Mathematics of Computing; Neural networks; Numerical analysis; Original Research; Tensors; Theory of Computation; 11B39; Convolution; Moore–Penrose inverse; 05A10; Generalized conditional sequence; 15A09; Conditional matrix
• ISSN: 1598-5865; 1865-2085
• DOI: 10.1007/s12190-023-01974-5

Moore–Penrose inverse emerges in statistics, neural networks, machine learning, applied physics, numerical analysis, tensor computations, solving systems of linear equations and in many other disciplines. Especially after the 2000s, the topic of Moore–Penrose inverse has started to attract great attention by researchers and has become a popular subject. In this paper, we investigate the Moore–Penrose inverse of the conditional matrices via convolution product formula. In order to use convolution formula effectively, we derive some useful identities by using some properties of the generalized conditional sequence. Moreover, we express the Moore–Penrose inverse of the conditional matrices in the form of block matrices. Finally, we not only present more general results compared to earlier works, but also provide many novel results using analytical techniques.