vector_spaces3

vector_spaces3 - BASIS and DIMENTION Nonrectangular...

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1 BASIS and DIMENTION Nonrectangular Coordinate Systems In plane analytic geometry we associate a point P in the plane with a pair of coordinates (a, b ) by projecting P onto a pair of perpendicular coordinate axes (Fig. 1a). Each point in the plane is assigned a unique set of coordinates, and conversely, each pair of coordinates is associated with a unique point in the plane. Although perpendicular coordinate axes are the most common, any two nonparallel lines can be used to define a coordinate system in the plane. For example, in Fig. 1b, we have attached a pair of coordinates (a, b ) to the point P by projecting P parallel to the non- perpendicular coordinate axes. Figure 1 Similarly, in 3-space any three noncoplanar coordinate axes can be used to define a coordinate system (Fig. 1c).
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2 To extend the concept of a coordinate system to general vector spaces, it will be helpful to reformulate the notion of a coordinate system in 2-space or 3-space using vectors rather than coordinate axes to specify the coordinate system.
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This note was uploaded on 06/20/2008 for the course AM 025b taught by Professor Kiruscheva during the Winter '07 term at UWO.

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vector_spaces3 - BASIS and DIMENTION Nonrectangular...

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