(Trick Question: ) What is 0 · u ?
If the "0" is a scalar (which the non-bold type indicates) then this operation makes no sense.
If the "0" means the zero-vector (which means the zero should have been in bold face) then the result is the scalar 0.
The dot product is also defined for the column matrices that represent two vectors. For two-dimensional column matrices the dot product is defined as:
Let a = ( a1, a2 )T
Let b = ( b1, b2 )T
Then the dot product is:
a · b = a1b1 + a2b2
Multiply corresponding elements of each column matrix, then add up the products. The result is a scalar value.
Sometimes the dot product of column matrices is written like this: aT b (but it is defined the same way). The reason for this second, odd notation will be apparent in a later chapter when matrix multiplication is discussed.
Here is an example: