vector_spaces3

# vector_spaces3 - BASIS and DIMENTION Nonrectangular...

This preview shows pages 1–3. Sign up to view the full content.

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).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

vector_spaces3 - BASIS and DIMENTION Nonrectangular...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online