Differentiation of non-hermitian matrix functions depending on a parameter

1965 ◽  
pp. 73-87 ◽  
Author(s):  
Ju. L. Daleckiĭ
Keyword(s):  
Hermitian Matrix ◽  
Matrix Functions

Perturbation of analytic hermitian matrix functions

1985 ◽  
Vol 20 (1-2) ◽  
pp. 23-48 ◽  
Author(s):  
I. Gohberg ◽  
P. Lancaster ◽  
L. Rodman
Keyword(s):  
Hermitian Matrix ◽  
Matrix Functions

Inertias and ranks of some Hermitian matrix functions with applications

2011 ◽  
Vol 10 (1) ◽  
pp. 329-351 ◽  
Author(s):  
Xiang Zhang ◽  
Qing-Wen Wang ◽  
Xin Liu
Keyword(s):  
Hermitian Matrix ◽  
Matrix Functions

scholarly journals Solving Optimization Problems on Hermitian Matrix Functions with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Xiang Zhang ◽  
Shu-Wen Xiang
Keyword(s):  
Optimization Problems ◽  
Hermitian Matrix ◽  
Sufficient Conditions ◽  
Positive Definite ◽  
Matrix Functions ◽  
Matrix Equations ◽  
Necessary And Sufficient Condition ◽  
System Of Matrix Equations ◽  
The Matrix ◽  
Necessary And Sufficient

We consider the extremal inertias and ranks of the matrix expressionsf(X,Y)=A3-B3X-(B3X)*-C3YD3-(C3YD3)*, whereA3=A3*,  B3,  C3, andD3are known matrices andYandXare the solutions to the matrix equationsA1Y=C1,YB1=D1, andA2X=C2, respectively. As applications, we present necessary and sufficient condition for the previous matrix functionf(X,Y)to be positive (negative), non-negative (positive) definite or nonsingular. We also characterize the relations between the Hermitian part of the solutions of the above-mentioned matrix equations. Furthermore, we establish necessary and sufficient conditions for the solvability of the system of matrix equationsA1Y=C1,YB1=D1,A2X=C2, andB3X+(B3X)*+C3YD3+(C3YD3)*=A3, and give an expression of the general solution to the above-mentioned system when it is solvable.

scholarly journals Numerical Optimization of Eigenvalues of Hermitian Matrix Functions

2014 ◽  
Vol 35 (2) ◽  
pp. 699-724 ◽  
Author(s):  
Emre Mengi ◽  
E. Alper Yildirim ◽  
Mustafa Kiliç
Keyword(s):  
Numerical Optimization ◽  
Hermitian Matrix ◽  
Matrix Functions
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