John Backus, 1924-2007

Posted in Computing 4 years, 10 months ago

John Backus died on Saturday. He was the father of FORTRAN, Turing Award winner, and one of the names behind the Backus-Naur form (Peter Naur, 2005 Turing Award winner, was the other).

His Turing Award lecture is also a remarkable read. Titled, “Can programming be liberated from the Von Neumann style,” it laid the groundwork for functional programming…

(via Geomblog)

Euler identity

Posted in Paper 4 years, 10 months ago

Another interesting paper came out last week on the preprint archive, “A matrix generalization of Euler identity.” The Euler identity reads,

e^{jx} = \cos(x) + j \sin(x)

and is traditionally derived from the Taylor expansion of sine and cosine. In this paper, the author generalizes the Euler identity to matrices. He does this by introducing a complex matrix, known as the imaginary unit matrix

\mathbf{\Phi} = \left( \begin{array}{cc} 0 & j \\j \alpha^2 & 0\end{array} \right)

Just like j^2 = -1, \mathbf{\Phi^2} = – \alpha^2 \mathbf{I}.

He then proves the Euler identity for these matrices as:

e^{x \mathbf{\Phi}} = \cos(\alpha x)\mathbf{I} + \frac{1}{\alpha} \sin(\alpha x) \mathbf{\Phi}

for all real x.

Tumblelogs

Posted in Web 4 years, 10 months ago

Through bbgm, I was introduced to the idea to Tumblelogs. I really like the format that is used to display content. I think limiting one post per page really helps focus the reading, and it doesn’t necessarily have to be short posts. I’m going to adopt this format for my blog over the next few months. Unfortunately, I’m currently swamped with work, so it’ll take atleast a month to see any changes on this site.