How does resizing an image affect the intrinsic camera matrix?
Note: That depends on what coordinates you use in the resized image. I am assuming that you are using zero-based system (like C, unlike Matlab) and 0 is transformed to 0. Also, I am assuming that you have no skew between coordinates. If you do have a skew, it should be multiplied as well 

Short answer: Assuming that you are using a coordinate system in which $u' = \frac{u}{2} , v' = \frac{v}{2}$, yes, you should multiply $a_x,a_y,u_0,v_0$ by 0.5.

Detailed answer The function that converts a point $P$ in world coordinates to camera coordinates  $(x,y,z,1)-&gt;(u,v,S)$ is:

$$ \left( \begin{array}{ccc}
a_x &amp; 0 &amp; u_0 \\
0 &amp; a_y &amp; v_0 \\
0 &amp; 0 &amp; 1 \end{array} \right)  
\left( \begin{array}{ccc}
R_{11}  &amp; R_{12} &amp; R_{13} &amp; T_x \\
R_{21}  &amp; R_{22} &amp; R_{23} &amp; T_y  \\
R_{31}  &amp; R_{32} &amp; R_{33} &amp; T_z \\
0  &amp; 0&amp; 0 &amp; 1 
\end{array} \right) 
\left( \begin{array}{ccc}
x \\
y  \\
z \\
 1 
\end{array} \right)
$$

Where $(u,v,S)-&gt;(u/S,v/S,1)$, since the coordinates are homogenous.

In short this can be written as 
$ u= \frac{m_1 P}{m_3 P} , v = \frac{m_2 P}{m_3 P}$
where $M$ is the product of the two matrixes mentioned above, and $m_i$ is the i'th row of the matrix $M$. (The product is scalar product).

Re-sizing the image can be thought of:

$$ u'=u/2, v'=v/2 $$

Thus

$$ u' = (1/2) \frac {M_1 P} {M_3 P}  \\
v' = (1/2) \frac {M_2 P} {M_3 P} 
$$

Converting back to matrix form gives us:

$$
\left( \begin{array}{ccc}
0.5 &amp; 0 &amp; 0 \\
0 &amp; 0.5 &amp; 0 \\
0 &amp; 0 &amp; 1 \end{array} \right) 
\left( \begin{array}{ccc}
a_x &amp; 0 &amp; u_0 \\
0 &amp; a_y &amp; v_0 \\
0 &amp; 0 &amp; 1 \end{array} \right)  
\left( \begin{array}{ccc}
R_{11}  &amp; R_{12} &amp; R_{13} &amp; T_x \\
R_{21}  &amp; R_{22} &amp; R_{23} &amp; T_y  \\
R_{31}  &amp; R_{32} &amp; R_{33} &amp; T_z \\
0  &amp; 0&amp; 0 &amp; 1 
\end{array} \right) 
\left( \begin{array}{ccc}
x \\
y  \\
z \\
 1 
\end{array} \right)
$$

Which is equal to 

$$ \left( \begin{array}{ccc}
0.5 a_x &amp; 0 &amp; 0.5 u_0 \\
0 &amp; 0.5 a_y &amp; 0.5 v_0 \\
0 &amp; 0 &amp; 1 \end{array} \right)  
\left( \begin{array}{ccc}
R_{11}  &amp; R_{12} &amp; R_{13} &amp; T_x \\
R_{21}  &amp; R_{22} &amp; R_{23} &amp; T_y  \\
R_{31}  &amp; R_{32} &amp; R_{33} &amp; T_z \\
0  &amp; 0&amp; 0 &amp; 1 
\end{array} \right) 
\left( \begin{array}{ccc}
x \\
y  \\
z \\
 1 
\end{array} \right)
$$

For additional information, refer to Forsyth, chapter 3 - Geometric camera calibration.