# ESL - Linear Model where output is a vector. Ch 2 Pg 11

In the terminology used in ESL, a vector is a column vector. Let output be a $$k$$-vector, i.e.$$Y=(Y_1,Y_2,\cdots,Y_K)^T$$Now please refer to following line on pg 12.

In general $$\hat{Y}$$ can be a $$K$$-vector, in which case $$\beta$$ would be a $$p \times K$$ matrix

Q1: Am I correct that the matrix representation of the linear model in above situation will be $${\hat{Y}}^T =X^T.\hat{\beta}$$

Q2: Why is there a hat i.e. ^ over $$\beta$$, what is the significance on that?

Thanks