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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

| |
(105) |

**Definition 2:** two operators **P** and **Q** are
complementary operators if
| |
(106) |

**Definition 3:** two operators **P** and **Q** are
mutually orthogonal if
| |
(107) |

**Definition 4:** two vectors **u** and **v** are
orthogonal if
| |
(108) |

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Stanford Exploration Project

5/5/2005