Speaker
Nancy Menzelthe
(University of Nevada, Reno)
Description
Given $1\le k\le n$, the $k$-numerical range of $A\in \mathbb{C}_{n\times n}$ is defined by
$$
W_k(A): = \left\{ \sum_{i=1}^k x_i^*Ax_i: x_1, \dots, x_k\ \mbox {orthonormal vectors in } \mathbb{C}^n\right\}\subset \mathbb{C}.
$$
Motivated by Davis' intuitive explanation of the Elliptical Range Theorem, we introduce two notions of multiplicity for points in $W_k(A)$, namely wedge multiplicity and projection multiplicity. The wedge multiplicity is related to the Grassmannian and the projection multiplicity is related to the set of rank $k$ orthogonal projectors. We present several results concerning each notion and provide examples illustrating these multiplicities. The corresponding real analogues $V_k(A)$ are also studied.
Authors
Nancy Menzelthe
(University of Nevada, Reno)
Pan Shun Lau
(University of Nevada Reno)
Tin-Yau Tam
(University of Nevada, Reno)