Note on Bounds for Eigenvalues using Traces

We show that various old and new bounds involving eigenvalues of a complex n x n matrix are immediate consequences of the inequalities involving variance of real and complex numbers.Comment: 13 page

Some generalisations of the inequalities for positive linear maps

We obtain generalisations of some inequalities for positive unital linear maps on matrix algebra. This also provides several positive semidefinite matrices and we get some old and new inequalities involving the eigenvalues of a Hermitian matrix

Positive Linear Maps and Perturbation bounds of Matrices

We show how positive unital linear maps can be used to obtain lower bounds for the maximum distance between the eigenvalues of two normal matrices. Some related bounds for the spread and condition number of Hermitian matrices are also discussed here

An inequality for tensor product of positive operators and its applications

We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor product of operators as words on certain alphabets (i.e., a set of letters). As applications of the operator inequality and by a multilinear approach, we show some matrix inequalities concerning induced operators and generalized matrix functions (including determinants and permanents as special cases).Comment: Linear Algebra and Appl. in pres

Positive linear maps and eigenvalue estimates for nonnegative matrices

We show how positive unital linear maps can be used to obtain some bounds for the eigenvalues of nonnegative matrices

Complementary upper bounds for fourth central moment with extensions and applications

We prove some inequalities involving fourth central moment of a random variable that takes values in a given finite interval. Both discrete and continuous cases are considered. Bounds for the spread are obtained when a given nxn complex matrix has real eigenvalues. Likewise, we discuss bounds for the spans of polynomial equations.Comment: 17 page

Some inequalities for central moments of matrices

In this paper we shall study noncommutative central moment inequalities with a main focus on whether the commutative bounds are tight in the noncommutative case, or not. We prove that the answer is affirmative for the fourth central moment and several particular results are given in the general case. As an application, we shall present some lower estimates of the spread of Hermitian and normal matrices as well.Comment: 12 page

Bounds on Spreads of Matrices related to Fourth Central Moment. II

We derive some inequalities involving first four central moments of discrete and continuous distributions. Bounds for the eigenvalues and spread of a matrix are obtained when all its eigenvalues are real. Likewise, we discuss bounds for the roots and span of a polynomial equation