Cartesian Space

Cartesian Space:

An Euclidean space with an standard orthonormal frame .

Orthogonal:

.

Normal:

.

Notation:

Specify the Standard Frame as .

As defined previously, points and vectors are

• Different objects.
• Have different operations.
• Behave differently under transformation.

Coordinates:

Use an ``an extra coordinate'':

• 0 for vectors: means
• 1 for points: means
• Later we'll see other ways to view the fourth coordinate.
• Coordinates have no meaning without an associated frame!
  • Sometimes we'll omit the extra coordinate ...
    point or vector by context.
  • Sometimes we may not state the frame ...
    the Standard Frame is assumed.