Jacob's posts

Post has attachment

Public

**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...

Post has attachment

Public

**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...

Post has attachment

Public

**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. ...

Post has attachment

Public

**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...

Post has attachment

Public

Post has attachment

Public

**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....

Post has attachment

Public

**Food Groups and Mathematics**

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

Post has attachment

Public

**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...

Post has attachment

Public

**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...

Post has attachment

Wait while more posts are being loaded