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Matrix multiplication October 24, 2012

Posted by mareserinitatis in math, older son, teaching.
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The older boy was working on matrix multiplication in math.  He got very testy with me: “Why do I even need to know this?”  I replied that it’s used all the time in calculus-based physics.  That disappointed him as he would like to take it some day.

He was super frustrated because the explanation on the computer was very…verbal.  Unfortunately, I couldn’t locate my favorite linear algebra book, so I tried to go through and explain it while making some diagrams.

He still had some problems and then kept asking if they were somehow related to Punnet squares.  Um…not really.

And then he made this diagram.

I have to admit that it’s not how I would think to multiply matrices…or at least I think there are easier representations.  (In my mind, at least.)  However, this did work in that it made sense to him, and once he had figured out enough to draw this, he was able to finish the rest of the problems on this concept.

This just goes to show that we don’t all think the same way, I suppose.  The way we think about things may not always be the easiest for someone else.

 

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Repost: Happy Talk like a Pirate Day! September 19, 2012

Posted by mareserinitatis in humor, math.
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(This is a repost from my old Livejournal blog.)

On this most holy holiday, where we all celebrate the day when His Noodliness touched us all (and which we observe to prevent more global warming), it’s important to remember what the day is truly about: transformation.

You’ll often hear Pastafarians (and their lesser imitators) say, “Arrrr!” What, you ask, could they be talking about?

It may not be obvious, but they are talking about Arrrr (R), which is the rotation matrix. (Note that this is quite different from the Matrix.)

As any good sea-faring pirate knows, rotation matrices are essential tools for navigation.

From the Most Holy Texts of Wolfram,

Any rotation can be given as a composition of rotations about three axes (Euler’s rotation theorem), and thus can be represented by a matrix operating on a vector,

We should remember, on this day, that a series of rotations can be accomplished by multiplying the matrices of each individual rotation together, thus resulting in a single rotation matrix (not Matrix) to describe the overall transformation that has been achieved.

And this concludes the sermon for today.


Jack sparrow contemplating which rotation matrices will be the most useful in his next ship-board adventure.

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