In the matrix representations, the entries encode the cost of following an edge.

For the reason of this non-associativity, octonions have no matrix representation.

The matrix representations of operators are also determined by the chosen basis.

This procedure is analogous to matrix representation of complex numbers.

Another matrix representation for a graph is the incidence matrix.

The normal equations can be derived directly from a matrix representation of the problem as follows.

Each of the four Maxwell's equations are obtained from the matrix representation.

For a given value of ℓ, the matrix representation is (2ℓ + 1)-dimensional.

Second, it must be shown that this is a matrix representation of the cross product for some .

The matrix representations of these operators are constructed as follows: