What is J in while calculating SST in multiple regression?

Question

I am little confused what actually is the J in the formula of the SST and SSR for multiple regression

SST= $Y^T\left[ 1-\frac{1}{n}J\right]Y$

SSR=$Y^T\left[ H-\frac{1}{n}J\right]Y$

Answer 1

$J$ is the matrix of all $1$s. i.e., let $$ \mathbf{1}=(1,1,...,1)^T\in \mathbb{R}^n, $$ then $$ J = \mathbf{1}\mathbf{1}^T. $$ While $\frac{1}{n}J$ can be called "means generating matrix", namely, for some $y=(y_1, y_2,...,y_n)^T \in \mathbb{R}^n$, then $$ \frac{1}{n}Jy= (\bar{y}_n, \bar{y}_n, ..., \bar{y}_n)^T, $$ which is an essential part of any sum of squares.