Dot
Product (also known as Inner or
Scalar Product)
The dot product
is a scalar number and so it is also known as the
scalar or
inner
product.
In a real vector space, the scalar product
between two vectors
is computed in the following way:
Besides, there is another way to define the inner product, if you know
the angle between the two vectors:
We can conclude that if the inner product of two vectors is zero, the
vectors are orthogonal.
In Matlab, the appropriate builtin function to determine the inner
product is 'dot(u,v)'.
For example, let's say that we have vectors u
and v,
where
u
= [1 0] and v
= [2 2]. We can plot them easily with the 'compass'
function in Matlab, like this:
x = [1 2]
y = [0 2]
compass(x,y)
x
represents the horizontal coordinates for each vector, and y
represents their vertical coordinates. The instruction 'compass(x,y)'
draws a graph that displays the vectors with components (x,
y)
as arrows
going out from the origin, and in this case it produces:
We can see that the angle between the two vectors is 45 degrees; then,
we can
calculate the scalar product in three different ways (in Matlab code):
a = u * v'
b = norm(u, 2) * norm(v, 2) * cos(pi/4)
c = dot(u, v)
Code that produces these results:
a = 2
b = 2.0000
c = 2
Note that the angle has to be expressed in radians, and that the
instruction 'norm(vector,
2)' calculates the Euclidian
norm of a vector
(there are more types of norms for vectors, but we are not going to
discuss them here).
From
'Dot Product' to home
From
'Dot
Product' to 'Matlab Examples'

