What is it called when a row matrix is "flipped" into a column matrix?

Transposition.

Even if a row matrix and a column matrix are the same dimension and contain the same elements, they are considered different types. A "T" superscript is used when a column matrix is written as a row of numbers. The first element of a column matrix is the one at the top of the column. The first element of a row matrix is the one at the left of the row.

Here are two ways of writing out
the *same column matrix*.
The elements of the column matrix have the same subscripts
no matter how the column matrix is displayed.

(2, 0, 5, 1)^{T}

A `T`

superscript on column matrix with means to flip the
column into a row, resulting in a row matrix.
(Some books use a lower-case `t`

.)

What is: `( 1, 2, 3 )`

?
^{T T}