Here is a Wikipedia about the Dot-Product, which includes the relevant section on Rotation. Given the first example- is it correct where it says "Notice that the rotation matrix R is assembled by using the rotated basis vectors u1, v1, w1 as its rows, and these vectors are unit vectors". My understanding of it would be that the rotated basis vectors are represented as the columns. The same applies in the second example- "If a1 is a row vector, rather than a column vector, then R must contain the rotated basis vectors in its columns, and must post-multiply a1". Isn't it that the rotated basis vectors are the rows? This seems wrong, can someone confirm this? Thanks in advance.