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

Here is a simple example from image processing (software engineering).
From an 8-bit grayscale image, one can compute the mean graylevel - a real number between 0 and 255.
One can also compute the histogram - an integer vector of length 256.
Note that it is also possible to compute the mean graylevel from the histogram.
There are 3 spaces and 3 maps forming a commutative triangle.
One could say in this case that the mean graylevel "factors through" the histogram.
The same is true if 'mean graylevel' is replaced by other simple image statistics, such as median or any other quantile.  Many image APIs, such as ImageJ's macro language, can compute the histogram very quickly.  So one can use that factorization to compute any quantile quickly too.
