Vector in vector notation

Question

I'm a bit confused as far as notationally differentiating between row and column vectors goes. Suppose I define a column vector

$$\boldsymbol{a} = (a_{1}, a_{2})^{T}$$

and another column vector

$$\boldsymbol{b} = (b_{1}, b_{2})^{T} \,.$$

Say that the column vector $\boldsymbol{c}$ is given by

$$\boldsymbol{c} = (a_{1}, a_{2}, b_{1}, b_{2})^{T}\,.$$

If I wanted to write that more concisely. Would it be $$\boldsymbol{c} = (\boldsymbol{a}, \boldsymbol{b})^{T}$$ or $$\boldsymbol{c} = (\boldsymbol{a}^{T}, \boldsymbol{b}^{T})^{T}\,?$$

Answer 1

If you agree with $(a_1,a_2,b_1,b_2) = ((a_1,a_2),(b_1,b_2))$, then it follows that

$$ \textbf{c}=(a_1,a_2,b_1,b_2)^T = ((a_1,a_2),(b_1,b_2))^T = (\textbf{a}^T, \textbf{b}^T)^T.$$