Such a basis of gamma matrices is not unique.

It is also possible to define higher-dimensional gamma matrices.

This defining property is considered to be more fundamental than the numerical values used in the gamma matrices.

This property of the gamma matrices is essential for them to serve as coefficients in the Dirac equation.

It is useful to define the product of the four gamma matrices as follows:

Although uses the letter gamma, it is not one of the gamma matrices.

The gamma matrices can be chosen with extra hermiticity conditions which are restricted by the above anticommutation relations however.

One can factor out the to obtain a different representation with four component real spinors and real gamma matrices.

The new basis vectors share the algebra of the gamma matrices but like above are usually not equated with them.

The Pauli and gamma matrices were introduced here, in theoretical physics, rather than pure mathematics itself.