We give several criteria that are equivalent to the basic singular value majorization inequality (1.1) that is common to both the usual and Hadamard products. We then use these criteria to give a uniied proof of the basic majorization inequality for both products. Finally, we introduce natural generalizations of the usual and Hadamard products and show that although these generalizations do not...

We deal with two recent conjectures of R.-C. Li [Linear Algebra Appl. 278 (1998) 317– 326], involving unitarily invariant norms and Hadamard products. In the particular case of the Frobenius norm, the first conjecture is known to be true, whereas the second is still an open problem. In fact, in this paper we show that the Frobenius norm is essentially the only invariant norm which may comply wi...

Let f(t) be a nonnegative concave function on 0 ≤ t < ∞ with f(0) = 0, and letX,Y be n×nmatrices. Then it is known that ‖f(|X+Y |)‖1 ≤ ‖f(|X|)‖1+‖f(|Y |)‖1, where ‖ · ‖1 is the trace norm. We extend this result to all unitarily invariant norms and prove some inequalities of eigenvalue sums.

We obtain a representation of unitarily invariant norm in terms of Ky Fan norms [1, p.35]. Indeed we obtain a more general result in the context of Eaton triple with reduced triple. Examples are given. 2000 Mathematics Subject Classification: 15A60, 65F35.

In this paper, we show a multiple-term refinement of Young?s type inequality and its reverse via the Kantorovich constants, which extends unifies two recent important results due to L. Nasiri et al. (Result. Math (74), 2019), C. Yang (Journal. Math. Inequalities, (14), 2020). An application these scalars give inequalities for operators, Hilbert-Schmidt norms, traces unitarily invariant norms.

Let M n (F) denote the space of matrices over the eld F. Given A2 M n (F) deene jAj (A A) 1=2 and U(A) AjAj ?1 assuming A is nonsingular. Let 1 (A) 2 (A) n (A) 0 denote the ordered singular values of A. We obtain majorization results relating the singular values of U(A + A) ? U(A) and those of A and A. In particular we show that if A; A2 M n (R) and 1 ((A) < n (A) then for any unitarily invaria...

In this work, we investigate inequalities of singular values and unitarily invariant norms for sums products matrices. First, give an another more concise clear proof to inequality obtained by Chen Zhang [6, Theorem 5]. Then, establish values. addition, also a As applications inequality, present some inequalities.