I have read Parenthesis vs brackets for matrices
and I currently use brackets matrices (quaternions in 3D computing, in fact).
But I still have a doubt about the strict compatibility of notations between brackets and parenthesis, as explained in the previous topic.
I do think brackets are orientation dependent where parenthesis are not, which goes with comas usage… It's my question
$$
\begin{pmatrix} 1, 2, 3, 6 \end{pmatrix}
·
\begin{pmatrix} 0, 1, 0, 0 \end{pmatrix}
=
\begin{pmatrix} -2, 1, 6, -3\end{pmatrix}
$$
but
$$
\begin{bmatrix}
1 \\
2 \\
3 \\
6
\end{bmatrix}
·
\begin{bmatrix}
0 \\
1 \\
0 \\
0
\end{bmatrix}
=
\begin{bmatrix}
-2\\
1\\
6\\
-3
\end{bmatrix}
$$
What's the truth ?
Best Answer
Sometimes it is a matter of agreement. Many analysts use $(x_1,\ldots,x_n)$ to denote vectors of $\mathbb{R}^n$, while geometers and algebraists recommend $$ \begin{pmatrix} x_1 \\ \vdots \\ x_n \end{pmatrix}. $$ Indeed analysts often confuse, in $\mathbb{R}^n$, vectors and co-vectors (i.e. linear forms acting on vectors).