Numerical Shadow

The web resource on numerical range and numerical shadow

User Tools

Site Tools


numerical-range:generalizations:c-numerical-range

C numerical range

Definition

Let $A$ be an $n \times n$ matrix and $(c_1, c_2, \ldots, c_n)$ be a real n-tuple. The c-numerical range of $A$ is the set ‡™…[1] $$ W_C(A) = \left\{ \sum_{j=1}^N c_j \bra{x_j} A \ket{x_j}: \{\ket{x_i}\}_{i=1}^N \mathrm{\;forms\; an\; orthonormal\; basis\; of\;} \mathbb{C}^N \right\} $$

1. Schulte-Herbruggen, T., Dirr, G., Helmke, U., Glaser, S. J., 2008. The significance of the C-numerical range and the local C-numerical range in quantum control and quantum information. Linear and Multilinear Algebra, 56, Taylor \& Francis, pp.3–26.
numerical-range/generalizations/c-numerical-range.txt · Last modified: 2014/10/15 00:26 by lpawela