Some Bounds for the Singular Values of Matrices
نویسندگان
چکیده
Abstract We know that to estimate matrix singular values ( especially the largest and the smallest ones ) is an attractive topic in matrix theory and numerical analysis. In this note, we first provide a simple estimate for the smallest singular value σn(A) of n × n positive definite matrix A. Secondly, we obtain some simple estimates for the smallest singular value σn(A) and the largest singular value σ1(A) of any n× n complex matrix A, which is not necessarily positive definite. Finally, we get a simple estimate for the largest singular value σ1(A) of an n× n nonsingular complex matrix A. These estimates are presented as a function of the determinant and the Euclidean norm of A and n.
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