Let $A_1,\dots,A_L$ be $N\times N$ hermitian matrices. Consider the problem \begin{align} \lambda^{\star}=\max_{}&\lambda_{min}\left(\sum_{i=1}^{L}r_iA_i\right) \\ &r_i\geq 0,~\sum_{i=1}^{L}r_i=1 \end{align} $\lambda_{min}(.)$ denotes the minimum eigenvalue of the argument matrix. I am familiar that this is a convex problem and am familiar with the tools to solve it. I am interested in studying the multiplicity of this minimum eigenvalue. Any pointers to literature related to such problems?

Take the 2-minute tour
×

MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.