Matrix Theory Transpose

#1
I'm studying General Linear Model, so I have to go over Matrix Theory. I don't get what is said below:



Shouldn't [tex]yy^T[/tex] be [tex]([n \times 1][1 \times n])[/tex]? and therefore be undefined because we can't do matrix multiplication here?? I thought matrix multiplication was not commutative.
 
#2
macro90 said:
Shouldn't [tex]yy^T[/tex] be [tex]([n \times 1][1 \times n])[/tex]? and therefore be undefined because we can't do matrix multiplication here?? I thought matrix multiplication was not commutative.
[tex]yy^T[/tex] = [tex]([n \times 1][1 \times n])[/tex], a [tex]n \times n[/tex] matrix.

Let's try a simple case where [tex]y^T[/tex] = (1,1).
[tex]yy^T[/tex] = [tex]\left( \begin{array}{cc}1 & 1\\1 & 1\\\end{array} \right) [/tex]

[tex]y^Ty[/tex]=2