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Analysis Seminar – Khalid Said, University of Alabama
April 29, 2019 @ 11:00 am - 12:00 pm
In this presentation we examine some useful properties of the numerical range. We explore
two dierent positions , generic and generalized generic positions. We show that two pairs of
subspaces (M,N) and (M?;N?) are unitarily equivalent if M and N are subspaces of Cn in
generic position by constructing a unitary operator. We establish the relationships between
two sets of the principal angles, the principal angles between M and N and the principal angles
between M? and N?. We use these relationships to compute the numerical range of the sum
of two orthogonal projections onto M and N.
Numerical Range, Projections, Generic position