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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}](img295.gif) |
(105) |
Definition 2: two operators P and Q are
complementary operators if
| ![\begin{displaymath}
{\bf P+Q} = {\bf I}.\end{displaymath}](img296.gif) |
(106) |
Definition 3: two operators P and Q are
mutually orthogonal if
| ![\begin{displaymath}
{\bf PQ} = {\bf QP} = {\bf 0}.\end{displaymath}](img297.gif) |
(107) |
Definition 4: two vectors u and v are
orthogonal if
| ![\begin{displaymath}
{\bf u'v}={\bf v'u}=0.\end{displaymath}](img298.gif) |
(108) |
Next: General properties of the
Up: Geometric interpretation of the
Previous: Geometric interpretation of the
Stanford Exploration Project
5/5/2005