Saturday, October 29, 2011
Hall 1-2 (San Jose Convention Center)
We take basic concepts from linear algebra and Banach algebras, such as notions of eigenvalues, eigenvectors, diagonalization, the spectrum and algebraic elements, and find their analogues in Mn(C[a,b]). Specifically, we explore the relationship of the spectrum of elements in Mn(C[a,b]) with the spectrum of elements in Mn(C) and show eigenvectors do not always exist for elements in the spectrum. We also provide a characterization of algebraic elements in Mn(C[a,b]). Finally, we give a construction for the diagonalization of certain Hermitian elements in M2(C[a,b]).