When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this entanglement can be described using the Schmidt decomposition. This selects a preferred orthonormal basis for expressing the wavefunction and gives a measure of the degree of entanglement present in the system. The extension of this to the more general case of *n* subsystems is not yet known. We present a review of this process using the standard representation and apply this method to the geometric algebra representation. This latter form has the advantage of suggesting a generalisation to *n* subsystems.

R.F. Parker and C.J.L. Doran, **Analysis of 1 and 2 Particle Quantum Systems using Geometric Algebra, **C. Doran, L. Dorst and J. Lasenby eds. *Applied Geometrical Alegbras in computer Science and Engineering, AGACSE 2001*, p. 213, Birkhauser (2002)