Using spike diagrams, go over the steps of taking the dot product
of the vectors (1,2) and (2,4).
2
Define the dot product of two functions and that
are defined for .
3
In what sense is the dot product between the earlier two vectors
similar to the inner product between the functions and
defined for ? In what fundamental sense is it different?
4
What do you need to do with dot products and inner products if
your vectors respectively functions become complex? If you do so,
what can you say about a dot/inner product of a vector/function
with itself?
5
When are vectors/functions orthogonal to each other?
6
Give three vectors in three dimensional space that form an
orthonormal set.
7
Give a set of two orthonormal functions defined on the interval
.