What's the formal way to map a Matrix $A \in M(n \times n, K)$ to a row vector B \in K^{n²} where
a) the columns
$col_i(A)\quad, \quad 1 \leq i \leq n$
are arranged one below the other
b) the rows
$row_i(A)\quad, \quad 1 \leq i \leq n$
are transposed and then arranged one below the other
How to define B? What's an/the endomorphism from $M(n \times n, K)$ to K^{n²} and backwards?