Notating the components of the $\hat{\beta}$ matrix when $\hat{Y}$ is multidimensional

Question

This is a question on The Elements of Statistical Learning. We have from the linear model $$\hat{Y} = X^{T}\hat{\beta}$$ where $\hat{Y}^{T} = \begin{bmatrix} \hat{Y}_1 & \hat{Y}_2 & \cdots & \hat{Y}_K \end{bmatrix}$, $X^{T} = \begin{bmatrix} 1 & X_1 & X_2 & \cdots & X_p \end{bmatrix}$. In the case where $K = 1$, the standard notation for the components of $\hat{\beta}$ is $$\hat{\beta} = \begin{bmatrix} \hat{\beta}_0 \\ \hat{\beta}_1 \\ \vdots \\ \hat{\beta}_p \\ \end{bmatrix}$$ Is there standard notation for the components of $\hat{\beta}$ for a general (positive integer) $K$?