As the problem loses symmetry, the final coefficient matrix is also not symmetric and hence the solver selection must be made carefully.

The coefficient matrix must be positive to ensure that the equation is trace-preserving and completely positive.

Very often, all the coefficients are written in the form of a matrix A, which is called a coefficient matrix.

The choice of relaxation factor ω is not necessarily easy, and depends upon the properties of the coefficient matrix.

Next, the quantized coefficient matrix is itself compressed.

The classification depends upon the signature of the eigenvalues of the coefficient matrix "a".

The state equations for a linear time invariant system can be expressed using coefficient matrices:

The biggest disadvantage is that it fails to take advantage of coefficient matrix to be a sparse matrix.

For an implicit method, the coefficient matrix is not necessarily lower triangular:

For the previous example, the coefficients of the equations can be stored in a coefficient matrix.