Abstract
In this chapter, we study the vector algebra of 3-dimensional space. The term “algebra” is meant here in its mathematical sense, so that in addition to the usual vector-space manipulations, an associative multiplication of vectors is required. Relatively simple considerations lead us to what is called the geometric algebra(or Clifford algebra)of 3dimensional space, also known as the Pauli algebra. The standard matrix representation of this algebra replaces basis vectors by Pauli spin matrices (and hence the name “Pauli algebra”), but specific representations encumber the mathematics with unnecessary baggage; it is usually simpler to work directly in the algebra in component-free notation without reference to any matrices.
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