Using dot-product instead of multiplying with transpose

Question

We have the following equation, that we want to implement into our code with arrays/matrices
h(x, y, z) = ax + by + cz

pseudeo code:

X = [a, b, c]  
A = [x, y, z]

Often I see the equation being implemented like this:

h = transpose(A) * T

Is there any difference of just using the dot product?

h = dotproduct(A, X)

Is there a specific reason why the transpose is used over the dotproduct?

Answer 1

Mathematically, there's no difference. In implementation- dotproduct(...) may actually be faster, since transpose(...) may eagerly move the elements around prior to the matrix multiplication, doing "unnecessary" work.