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Definitions

I give a set of definitions that will help us to better understand the properties of the noise and signal filters in equation ([*]).

Definition 1: an operator P is a projector if
\begin{displaymath}
{\bf PP} = {\bf P}.\end{displaymath} (105)
Definition 2: two operators P and Q are complementary operators if
\begin{displaymath}
{\bf P+Q} = {\bf I}.\end{displaymath} (106)
Definition 3: two operators P and Q are mutually orthogonal if
\begin{displaymath}
{\bf PQ} = {\bf QP} = {\bf 0}.\end{displaymath} (107)
Definition 4: two vectors u and v are orthogonal if
\begin{displaymath}
{\bf u'v}={\bf v'u}=0.\end{displaymath} (108)


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Next: General properties of the Up: Geometric interpretation of the Previous: Geometric interpretation of the
Stanford Exploration Project
5/5/2005