created 08/26/97; revised 08/12/00; 07/23/03
CHAPTER 8 — Length, Orthogonality, and the Column Matrix Dot Product
This chapter discusses two important facts:
(1) The dot product
of a column matrix with itself returns
the square of the
length of the vector it represents.
(2) The dot product of two column matrices that represent
orthogonal vectors is zero.
- The dot product and vector length.
- Unit vectors.
- Unit normal.
- Dot products of orthogonal vectors and of their column matrices.
- How to construct a vector orthogonal to a given vector.
Let v = ( 3, 4 )T
- v · v = ?
- The length of v = ?