This is the summary of a presentation given at the Joint Mathematics Meetings, January 10-13, 1996, Orlando, Florida.

One of the topics included in most first courses in linear algebra concerns the representation of elements of a vector space as coordinate vectors relative to a basis. When the vector space is R^n and vectors are already expressed as column matrices, this topic is particularly confusing. Students commonly ask why anyone would want to use any basis other than the standard one to represent vectors in this context. This presentation will feature several natural examples from applications in astrodynamical modeling. The general setting involves a sensor that detects and reports objects (stars, satellites) relative to a natural local coordinate system. That is, the observations are reported as coordinate vectors relative to a basis that is specific to the sensor. To combine observations of this type from distinct sensors requires converting between representations relative to different bases. A similar conversion is necessary to make the observations compatible with motion models that are formulated in an idealized inertial space. These examples demonstrate that the use of nonstandard bases can be very natural, and illustrate the importance of converting between alternate basis representations.

Dan Kalman, American University