Now I have something like this: $$p\beta^T\beta+q\beta^TX^TX\beta$$ where p and q are constants and $\beta$, X are matrices. I want to do something like this: $$\beta^2(p+qX^2)$$ Is this right?
My thought is that since $\beta X^TX\beta$ is just $(\beta X)^2$, so this is ok.
If this is wrong, can anybody tell me what is the right way to do a similar thing like extracting $\beta$?
Please help! I don't know where I can find any formulas for this.
If you were to extract $\beta$, you need to extract it to behind the parenthesis. @tch is right. Also note that, only $||X||^2_2 = X^TX$