When constructing an orientation matrix, are the rows of the matrix the axis?

Question

When constructing an orientation matrix, are the rows of the matrix the axis?

The matrix is row-major and I'm multiplying vectors on the right (Mv). So, the matrix looks like

r0c0 r0c1 r0c2
r1c0 r1c1 r1c2
r2c0 r2c1 r2c2

Answer 1

From a mathematical point of view, it depends on in which order you are multiplying the vectors with the matrix.

• Using a row-vector (v) and multiplying it with a matrix (A) as v∙A, then the rows will act as the axes.
• Using a column-vector (v) and multiplying a matrix (A) with it as A∙v, then the columns will act as the axes.

Answer 2

That depends, if it is in row major form then yes, for column major form no.

Where does this matrix come from?