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Jacob Mazor
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Cayley-Hamilton Theorem Part III
In order to establish the Cayley-Hamilton theorem we first show the following result. Proposition The set of diagonalizable linear transformations on finite dimensional complex space is dense in the set of all linear operators on that space. Before we are a...

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Cayley-Hamilton Theorem II: The Arzela-Ascoli Theorem
In the previous post , we gave ourselves an incredibly useful measuring stick for vectors and linear operators. We now look at some general results regarding the convergence of sequences of functions, in order to build towards the Cayley-Hamilton Theorem. L...

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Cayley-Hamilton Theorem Part I: Norms
In this and a following blog post, I will explain and prove the Cayley-Hamilton theorem, a main algebraic result of linear operators. There are of course multiple proofs which can be found online, the vast majority of which approach it via algebraic means. ...

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How to write if you're a mathematician, scientist, or an engineer: Part 1 - Proofs
Hey all. I started college recently, and something that I've found is that writing is important . To many of you this might seem obvious, but for those of you who didn't know, writing is possibly the most important form of communication that you'll have, ev...

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A Process Completed
Over the past few months a majority of my time was dedicated to the college application process. I've received all my decisions, and wanted to share the essay that I sent to the University of Chicago. I picked a "choose your own prompt" and had fun with it....

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Food Groups and Mathematics
Mr Lovenstein combines mathematics and health as he demonstrates geometrically stable food groups.

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Cookie Physics: Problem 3
So far I haven't received any answers for my first two problems. This week I'm toning down the difficulty a bit. Imagine a setup similar to the image shown to the left. Assume m 2 = 2kg and that the string has a constant linear mass density of μ and a lengt...

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Problem of the Week 1: Canon Projectile
Here's the challenge:

You fire a ball from a cannon across a field. While the ball is inside the cannon it accelerates at a rate of a = 5/(r+0.5) 2 in m/s 2 , where r is the distance down the tube of the cannon that the ball has traveled in meters. Compute...

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