# Dot Product of Vector with matrix components

In Physics it's common to write matrices in vector components to simplify notation. This commonly occures with the pauli vector $$\vec\sigma = \begin{pmatrix}\sigma_1 & \sigma_2 & \sigma_3\end{pmatrix}^\mathrm{T}$$

Then the scalar product $$\vec \sigma \cdot \vec p$$ with any vector p would be $$\sigma_1 p_1 + \sigma_2 p_2 + \sigma_3 p_3$$.

How would I implement such a product in Mathematica? Sure, I could use something like

paulivector = Table[PauliMatrix[k],{k,1,3}];
vector = {p1,p2,p3};

Sum[paulivector[[k]].vector[[k]],{k,1,3}];


But this doesn't seem to be the Mathematica way. I tried

Inner[Times,paulivector,vector]
Inner[Dot,paulivector,vector]


which resulted in:

Inner::incom: Length 2 of dimension 3 in {{{0,1},{1,0}},{{0,-I},{I,0}},{{1,0},{0,-1}}} is incommensurate with length 3 of dimension 1 in {px,py,pz}.

Is there a built-in function that I can use for this case?

Related (but 8-9 years old): A matrix-vector cross product

σ = Array[PauliMatrix, 3]