Usually in math classes, few real-world examples are explored with students. Generally, the books contain artificial examples in which just a contextualization of some calculation is presented. What I seek here are more elaborate examples, connected with modeling of several engineering.
For spatial mathematics, including environmental modeling, the kriging estimation method (as well most methods in geostatistics) relies on finding the weights for it's samples trought the solution of A*w=B system, the kriging system. The criteria for the solution is that the model of anisotropy given by the user is followed in the estimation.
In the same procedure it is very common to use rotation matrices to make compatible two different spatial entities of data (point and grid or mesh, for example).
Also I believe linear algebra is commonly used in most physical engines, including scientific DEM methods to calculate force, velocity, etc., by means of direction. In fact is so common that most probably the same is used in robotics.
I've actually googled it, (http://commons.bcit.ca/math/examples/robotics/linear_algebra/) and in here you can see they use algebra to handle several different coordinate systems in the same machine.
Are you asking for some computer application or Numerical Calculation in the class room?
Dear prof. Ganesh: both applications are interesting. thanks again, C.
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