Archive for March, 2007

CRT Revenues

Posted in Business 4 years, 10 months ago

I remember how expensive flat screen televisions were a couple of years back. These days it’s hard to find a CRT if you want to buy one.

crt.png

(via digitimes)

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.