Combined matrices and conditioning

作者：

Highlights：

• In this work we have introduced the reduced combined matrix by the normalized column matrix and the normalized row inverse matrix.

• Properties and relationships between the combined and the reduced combined matrix are given.

• That lower bound is constructed by the reduced combined matrix, concretely with the sum of its columns.

• Moreover, properties of the lower bound are given, concretely, the lower bound is 1 for unitary matrices in which case the lower bound is sharp.

摘要

•In this work we have introduced the reduced combined matrix by the normalized column matrix and the normalized row inverse matrix.•Properties and relationships between the combined and the reduced combined matrix are given.•That lower bound is constructed by the reduced combined matrix, concretely with the sum of its columns.•Moreover, properties of the lower bound are given, concretely, the lower bound is 1 for unitary matrices in which case the lower bound is sharp.

论文关键词：Combined matrix,Reduced combined matrix,Condition number

论文评审过程：Received 3 March 2021, Revised 3 July 2021, Accepted 23 July 2021, Available online 12 August 2021, Version of Record 12 August 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126549