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The lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices
The paper mainly discusses the lower bounds for the rank of matrices and sufficient conditions for nonsingular matrices. We first present a new estimation for [Formula: see text] ([Formula: see text] is an eigenvalue of a matrix) by using the partitioned matrices. By using this estimation and inequa...
| Autores principales: | , |
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| Formato: | Online Artículo Texto |
| Lenguaje: | English |
| Publicado: |
Springer International Publishing
2017
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| Materias: | |
| Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5519689/ https://www.ncbi.nlm.nih.gov/pubmed/28794607 http://dx.doi.org/10.1186/s13660-017-1446-4 |
| Sumario: | The paper mainly discusses the lower bounds for the rank of matrices and sufficient conditions for nonsingular matrices. We first present a new estimation for [Formula: see text] ([Formula: see text] is an eigenvalue of a matrix) by using the partitioned matrices. By using this estimation and inequality theory, the new and more accurate estimations for the lower bounds for the rank are deduced. Furthermore, based on the estimation for the rank, some sufficient conditions for nonsingular matrices are obtained. |
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