1 Introduction and PreliminariesIt is well known that the smallest singular value of a matrix is important in matrixthoery and applications.Varah and Qi,Johnson gave some results on lower bound of thesmallest singular value[1—4].Here,we use the block partitioned form of a matrix to ob-tain generalized lower bounds for σn(A).Furthermore,by scaling with a matrix D we ob-tain a new lower bound for σA of matrices which are not positive definite matrices.
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