I'm just reading a book on econometrics and now I'm stuck with a problem:

There is a Theorem on "Orthogonal Partitioned Regression" which says:

> 
> "In the multiple linear least squares regression of $y$ on two sets of variables $X\_1$ and $X\_2$, if the two sets of variables are orthogonal, then the separate coefficient vectors can be obtained by separate regressions of $y$ on $X\_1$ alone and $y$ on $X\_2$ alone. ..."
> 
> 
> 

Furthermore, the authors says that $X\_1$ and $X\_2$ are orthogonal if:
$$
(X\_1)' X\_2=0 \, ,
$$
which confuses me because so far I always thought the condition for orthogonality between two matrices is that $(X\_1)' X\_2=I$.

The book is: W. Greene, Econometric Analysis, 7th ed. / Theorem 3.1 / p.33

What I found so far is:

[Link 1](https://math.stackexchange.com/questions/148195/orthogonal-matrices) and [Link 2 (search for: "imagine")](http://www.le.ac.uk/users/dsgp1/COURSES/LEIMETZ/PARTIMOD.pdf), but neither really helps me with my problem.

BR
Fabian