Tag Archives: matrix multiplication

QM 101: Bra-Ket Notation

When I was in high school, bras were of great interest to me — mostly in regards to trying to remove them from my girlfriends. That was my errant youth and it slightly tickles my sense of the absurd that they’ve once again become a topic of interest, although in this case it’s a whole other kind of bra.

These days it’s all about Paul Dirac’s useful Bra-Ket notation, which is used throughout quantum mechanics. I’ve used it a bit in this series, and I thought it was high time to dig into the details.

Understanding them is one of the many important steps to climb.

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Sideband #71: Matrix Math

There are many tutorials and teachers, online and off, that can teach you how to work with matrices. This post is a quick reference for the basics. Matrix operations are important in quantum mechanics, so I thought a Sideband might have some value.

I’ll mention the technique I use when doing matrix multiplication by hand. It’s a simple way of writing it out that I find helps me keep things straight. It also makes it obvious if two matrices are compatible for multiplying (not all are).

One thing to keep in mind: It’s all just adding and multiplying!

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Sideband #64: Matrix Magic

In the last installment I introduced the idea of a transformation matrix — a square matrix that we view as a set of (vertically written) vectors describing a new basis for a transformed space. Points in the original space have the same relationship to the original basis as points in the transformed space have to the transformed basis.

When we left off, I had just introduced the idea of a rotation matrix. Two immediate questions were: How do we create a rotation matrix, and how do we use it. (By extension, how do we create and use any matrix?)

This is where our story resumes…

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Sideband #63: Matrix Rotation

For me, the star attraction of March Mathness is matrix rotation. It’s a new toy (um, tool) for me that’s exciting on two levels: Firstly, it answers key questions I’ve had about rotation, especially with regard to 4D (let alone 3D or easy peasy 2D). Secondly, I’ve never had a handle on matrix math, and thanks to an extraordinary YouTube channel, now I see it in a whole new light.

Literally (and I do mean “literally” literally), I will never look at a matrix the same way again. Knowing how to look at them changes everything. That they turned out to be exactly what I needed to understand rotation makes the whole thing kinda wondrous.

I’m going to try to provide an overview of what I learned and then point to a great set of YouTube videos if you want to learn, too. Continue reading