# Recent Posts - What I've been saying

## Pebble App – App Manager

I recently got a Pebble as a present from my lovely girlfriend and I’ve been toying with the idea of creating an app for it, partly for fun and partly to support the awesome work that I think the guys at Pebble are doing.

I’m aiming to help resolve what I feel is one of the major issues with the Pebble framework at the moment, which is its fixed address app structure. For those who don’t know; you can currently only install a maximum of 8 apps/watchfaces on the watch at any one time regardless of how much space each app or watchface takes up, this means that whilst your Pebble has a storage capacity of 800KB, the majority of that space is likely wasted.

The primary goals of the app can be summarized as follows: Read more »

## Proving the det(AB) = det(A)det(B) relation using the Levi-Cevita tensor

I recently had to prove that $$\det(\mathbf{A}\mathbf{B}) = \det(\mathbf{A})\det(\mathbf{B})$$

I thought that it would be an interesting exercise to show this using the standard definition of the determinant of a matrix that physicists usually give (using Einstein summation):

$$\det(\mathbf{A}) \triangleq \varepsilon^{i_{1}\cdots i_{n}} a_{1 i_{1}} \cdots a_{n i_{n}}$$

We note that if we denote $\mathbf{C} = \mathbf{A}\mathbf{B}$, then we have $c_{ij} = a_{ik}b_{kj}$, and thus:

\begin{align*}\det(\mathbf{C}) &= \varepsilon^{i_{1}\cdots i_{n}}c_{1 i_{1}}\cdots c_{n i_{n}} \\ &= \varepsilon^{i_{1}\cdots i_{n}} a_{1 k_{1}}b_{k_{1} i_{1}} \cdots a_{n k_{n}}b_{k_{n} i_{n}} \\ &= a_{1 k_{1}}\cdots a_{n k_{n}} \varepsilon^{i_{1} \cdots i_{n}}b_{k_{1} i_{1}}\cdots b_{k_{n} i_{n}}\end{align*}

## Welcome to my blog!

Hello everyone,

I’ve finally got around to creating my own website (2 years after coming up with the design!), it was a long process and it’s still not completely finished, but I’m hoping that having it up will encourage me to speed up the development process.

I’m hoping to blog about all sorts of matters that interest me, so ranging from generic posts about what’s going on in the world to software development related stuff to rants about Physics and Maths.

At the moment I’ve not developed the comments section of WordPress, but hopefully I should have designed and implemented that in the next couple of weeks; in the meantime, if you want to contact me you can use the “Contact Me” form at the bottom of the page or email me at admin@thomas-russell.co.uk (here’s hoping I don’t get too much spam!)

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