AFAIK, a vector can be specified using either "ordered set notation" or "matrix notation"
Ordered set notation
Matrix notation of row and colum vectors
I wonder if a column vector can be specified using ordered set notation. For example, can a column vector
$$
\begin{bmatrix}
1\\
2\\
3
\end{bmatrix}
$$ be specified as follows?
$$(1,2,3)$$
Plus, is the following statement correct?
A set {(1,0,0), (1,1,0), (1,0,1)} is a basis of column space of the matrix
\begin{bmatrix} 1&2&1&1\\ 0&0&1&0\\ 0&0&0&1 \end{bmatrix}.
Best Answer
I think that the column vector $\begin{bmatrix} 1\\ 2\\ 3 \end{bmatrix}$ and the ordered set $(1,2,3)$ represent the same element of the same linear space.
However, AFAIK, a set can't be seen as a basis minor of a matrix just because of the determinant minor definition.