Three-phase electrical systems (AC systems) have been traditionally represented by real-valued linear multiple-input/multiple-output (MIMO) systems or by complex-valued single-input/single-output (SISO) systems. The complex representation has the advantage to reduce the order of the model at the expenses of introducing a non-linearity when the AC system is unbalanced, which makes the analysis and control design tasks difficult. Recently, the application of geometric algebra (GA) has shown that the same AC system can be represented by a GA-valued linear SISO model. However, the simplicity (given by the order reduction and linearity) comes with a price: the lack of standard control analysis and design tools applicable to the model expressed in the GA domain. To help overcoming this difficulty, and in the context of AC systems, this chapter revisits the well-known singular value decomposition (SVD) of a linear MIMO system and derives the same decomposition for the GA-valued SISO system, namely, GA-SVD. Explicit formulas are presented for computing the singular values, the singular eigenvectors, and the three matrices that compose the GA-SVD. Additionally, its key geometrical components, namely, rotation, rescaling, and rotation, are also identified. An AC circuit example is presented to illustrate all the key findings.