How can an engineer make use of commutative diagram? I am in engineering and I have being awed by commutative diagram my entire life. But I do not see the purpose in knowing commutative diagram as arises in linear algebra?
Is there something in engineering that can be describe by commutative diagram? For example, operators such as laplace transform and fourier transform to map stuff to different spaces? Or expectation operator...
Thanks

A commutative diagram is simply a graphic device to represent the fact that two or more compositions of functions are equal.
There is no reason why an engineer will not have two compositions of functions and want to express that they are equal.
There is absolutely nothing mysterious in commutative diagrams. Sometimes they are a bit complicated, like

or even much more, but that is just because this diagram represents the fact that quite a few compositions are equal: each arrow represents a function, each path in the diagram represents the composition of the functions corresponding to the arrows it involves, and the commutativity of the diagram means simply that every time you pick two paths from one of the letters to another, the corresponding compositions are equal.
