Yes, the order of the vectors in the dot product matters. The dot product is defined as the sum of the element-wise products of the two vectors. If you switch the order of the vectors, the element-wise products will be different, and therefore the dot product will also be different. Here's an example:
Suppose we have two vectors a
and b
with the following elements:
a = [1, 2, 3]
b = [4, 5, 6]
If we take the dot product of a
and b
in the standard order, we get: