This is a lecture note of my joint work with Chi-Kwong Li concerning various results on the norm structure of n × n matrices (as Hilbert-space operators). The main result says that the triangle inequality serves as the ultimate norm estimate for the upper bounds of summation of two matric...
We show some upper bounds for the product of arbitrarily selected singular values of the sum of two matrices. The results are additional to our previous wo... BY Xi,FZ Zhang - 《Acta Mathematica Sinica English》 被引量: 0发表: 2023年 Some Inequalities for Sum of the Matrices The purpose...
If A,BA,B are real, then we must add the fact that the eigenvalues of the considered matrices are real or pairwise conjugate. Now I do not think that your condition A.vect(1)=0A.vect(1)=0 adds some useful information. EDIT. About the David's post. Let A,B∈Mn...
A remark on the characterization of the parallel sum of two matrices, Linear and Multilinear Algebra 22 (1987), no. 2, 193-197.A remark on the characterization of the parallel sum of two matrices, Linear and Multilin- ear Algebra 22 (1987), no. 2, 193-197....
Example 2: Finding the Sum of Matrices Find the sum of AA and B,B, given A=[abcd] and B=[efgh]A=[abcd] and B=[efgh] Solution Add corresponding entries. A+B=[abcd]+[efgh] =[a+eb+fc+gd+h]A+B=[abcd]+[efgh] =[a+eb+fc+gd+h] Example 3: Adding Matrix A and Ma...
In this paper,we obtain representations for the Drazin inverses of the sum of two matrices. According to thinking of a block matrix split into two triangular matrices,the different prove of the representations for Drazin inverse of the sum of two matrices were given using the property of Drazin...
This paper is about the relation of random matrix theory and the subordination phenomenon in complex analysis. We find that the resolvent of the sum of two random matrices is approximately subordinated to the resolvents of the original matrices. We estimate the error terms in this relation and in...
Some Results for the Drazin Inverses of the Sum of Two Matrices and Some Block Matrices[J] . Abdul Shakoor,Hu Yang,Ilyas Ali,Kazutake Komori.Journal of Applied Mathematics . 2013A. Shakoor, H. Yang, I. Ali, Some results for the Drazin inverses of the sum of two matrices and some ...
I have two sample covariance matrices, computed from nn samples, less than pp variables: they are singular then. I know that the sum of two covariance matrices is also a covariance matrix. My question is, if both are singular, is this sum also singular? And if both are not sing...
Much like the order of operations, sometimes called PEMDAS or BIDMAS, we should begin here by completing the part inside the parentheses. That’s the sum of 𝐴 and 𝐵. We can add matrices of the same size — that’s here two-by-two matrices — by simply adding the individual element...