We first present an inequality for the Frobenius norm of the Hadamard product of two any square matrices and positive semidefinite matrices. Then, we obtain a trace inequality for products of two positive semidefinite block matrices by using 2 × 2 block matrices.
By an embedding approach and through tensor products, some inequalities for generalized matrix functions (of positive semidefinite matrices) associated with any subgroup of the permutation group and any irreducible character of the subgroup are obtainned.
Let us define A = C r (a 0 , a 1 , . . . , a n-1 ) to be a n × n r-circulant matrix. The entries in the first row of A = C r (a 0 , a 1 , . . . , a n-1 ) are(i = 0, 1, 2, . . . , n -1), where P i and Q i are the ith Pell and Pell-Lucas numbers, respectively. We find some bounds estimation of the spectral norm for r-Circulant matrices with Pell and Pell-Lucas numbers.
We propose diverse upper bounds for the solution matrix of the continuous algebraic Riccati matrix equation (CARE) by building the equivalent form of the CARE and using some matrix inequalities and linear algebraic techniques. Finally, numerical example is given to demonstrate the effectiveness of the obtained results in this work as compared with some existing results in the literature. These new bounds are less restrictive and provide more efficient results in some cases.
The purpose of this paper is to present some new versions of Hermite-Hadamard type inequalities for operator convex functions. We give refinements of Hermite-Hadamard type inequalities for convex functions of self-adjoint operators in a Hilbert space analogous to well-known inequalities of the same type. The results presented in this paper are more general than known results given by several authors. MSC: 26D15; 47A63
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