February 2014
Intermediate to advanced
300 pages
11h 15m
English
Content preview from Iterative Optimization in Inverse Problems
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96 Iterative Optimization in Inverse Problems
7.5 Affine Linear Operators
It may not always be easy to decide if a given operator is averaged.
The class of affine linear operators provides an interesting illustration of
the problem.
Definition 7.3 An operator T : R
J
→ R
I
is affine linear or just affine if
there is an I by J matrix B andafixedvectord so that Tx = Bx + d for
all x.
TheaffineoperatorTx= Bx+d will be ne, sc, fne, or av precisely when
the linear operator given by multiplication by the matrix B is the same.
7.5.1 The Hermitian Case
When B is Hermitian, we can determine if B belongs to these classes
by examining its eigenvalues λ. We have the following theorem. ...
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