Recall the definitions of the complex number addition
and multiplication.
- Example 2.1
For instance, and .
Handling scalar operations with those rules, all of
the operations that we've covered
for real vector spaces carry over unchanged.
- Example 2.2
Matrix multiplication is the same, although the scalar arithmetic involves more
bookkeeping.
-
Everything else from prior chapters that we can,
we shall also carry over unchanged.
For instance, we shall call the ordered set of vectors
the standard basis for as a vector
space over and again denote it
.