It is months into the semester and Dr. Ferrar just recently dropped a bomb on the class about the implications of the inverse [A] matrix. We have been studying linear systems that can be described as:

[A][x] = [b],

where [A] is the parameters of the system, [x] and [b] are blah blah blah. One can solve for the desired unknowns [x] by multiplying inverse [A] by [b]:

[x] = [A]^{-1}[b]

I must admit, I am sick of writing out and describing this very practical relationship. However, a few days ago, Dr. Ferrar decided to impart some wisdom he has been holding on to for a very long time. And it has renewed my interest in the course.

[A]^{-1} just so happens to detail the degree to which each input of [b] effects the system and alters the outcome. It describes the relationship strength between elements of the system. For more visual interpreters, the sensitivity can also be illustrated in Matlab similar to the following.

With knowledge of sensitivity, an engineer can optimize a system and take control of how that system responds. From the above sensitivity matrix, one can see that the top left (00) responds very strongly to input, while the bottom left and top right edges do not. Very fascinating stuff.

And oh, doing Cholesky Factorization by hand is a pain in the [A]^{-1}ss.

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This is my favorite post so far in the semester. For one I wish I had the energy to actually write a post that relates to class. Luckily the latest imagesc command provides interesting visuals for a blog.

Also feel your pain on the Cholesky….

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Oh wow, thanks! I just left a comment about this on your most recent post.

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wow man you really put the time and effort in these blogs. i wish and i need to be more organized.

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Thanks. I try to make my posts somewhat worthwhile. You can make more meaningful posts by setting aside the time to develop ideas from your classes.

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Hahaha I see what you did there. Also they best part of engineering is when you can connect what youre learning to other things.

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I appreciate the fact that you put much more thought and time than most of us into your blogs. It makes it interesting to do these blog comments when the blog you are reading is much more interesting.

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I agree sensitivity is one of the more interesting topics we explored this semester. I love the visualization of the concept too. The grids generated are beautiful.

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