The lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices
Dafei Wang, Xumei Zhang
Journal of Inequalities and Applications · 2017
doi:10.1186/s13660-017-1446-4 (opens in a new tab)
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Abstract
Abstract 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 ∑ i = 1 n | λ i | 2 $\sum_{i=1}^{n} \vert \lambda_{i} \vert ^{2}$ ( λ i $\lambda_{i}$ 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.
Abstract licence: CC BY-NC-ND
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