Why the G matrix is 4*4?

[Originofamonia]

Hello,

Can I ask why the G matrix is a [4, 4] matrix instead of [3, 3]? I thought it's going to transform the coordinates from source to template?

Thanks.

[henryJhonOt]

A rigid transformation consists of a rotation transformation R(3x3) and a translation vector t(3x1). Together they form a 3x4 (R, t) or a matrix G(4x4) with the last row is fixed to 0, 0, 0, 1