Linear algebra, analogy with

The definition of the determinant of a linear operator is analogous to the definition of the trace. We start with the determinant of a matrix, which should be familiar from a Unear or abstract algebra textbook such as Artin [Ar, Section 1.3], It is a fact of linear algebra that det(AB) = (det A)(det B) for any two square matrices A and B of the same size. Hence for any matrices A and A related by Equation 2.5, we have... 

The systematic approach described above for solving radiation heal transfer problems is very suitable for use with today s popular equation solvers such as lili.V, Mathcad, and Matlab, especially when there are a large number of surfaces, and is known as the direct melhod (formerly, the matrix method, since it resulted in matrices and the solution required a knowledge of linear algebra). The second method described below, called the network method, is based on Ihe electrical network analogy. 

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