When we talk about a 4 X 4 matrix containing translation, rotation, and scale, it's important to realize that all of that information lives somewhere in the matrix. The following figure demonstrates how data is packed into the components of a 4 X 4 matrix:
The preceding figure demonstrates how data is packed into a Row Major matrix. This is called a Row Major Matrix because all three of the rotation basis vectors, as well as the translation vecto, are stored in the rows of the matrix. There is another notation to store the same data in a 4 X 4 matrix: Column Major notation. The following figure demonstrates how the same data is stored in a Column Major matrix:
It is important to note that the indexing of the matrix did not change between the row and column major notations. This is because the major of a matrix does not affect the definition of what a matrix is! The only thing the major of a matrix describes is in which elements the rotation, translation, and scaling data are...