Representations and symbolic computation of generalized inverses over fields

作者：

Highlights：

• An extension of the Urquhart formula is proposed.

• An algorithm for obtaining generalized inverses is proposed on the basis of proposed representations.

• New approach in symbolic computation of outer generalized inverses over fields of rational functions is proposed.

• We propose algorithms for symbolic computation of generalized inverses of matrices with functional entries over a field with or without an involution.

摘要

•An extension of the Urquhart formula is proposed.•An algorithm for obtaining generalized inverses is proposed on the basis of proposed representations.•New approach in symbolic computation of outer generalized inverses over fields of rational functions is proposed.•We propose algorithms for symbolic computation of generalized inverses of matrices with functional entries over a field with or without an involution.

论文关键词：Outer inverse,Inner inverse,Matrix equation,Computer algebra,Specialization of matrices,Matrices with functional entries

论文评审过程：Received 22 June 2020, Revised 28 February 2021, Accepted 11 April 2021, Available online 27 April 2021, Version of Record 27 April 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126287