Alan Dao's personal blog

Euler’s formula understanding is fundamental to the understanding of Rotary Positional Embedding (RoPE) implementation in model like LLaMA. Below is the proof of Euler’s formula that is used in my blog again and again for referrence purpose. Euler’s formula, often expressed as $$ e^{ix} = \cos(x) + i\sin(x) $$ is a fundamental result in complex analysis and connects trigonometric functions with the exponential function. It was discovered by Leonhard Euler in the 18th century.

Hello Neo here Ha! Got you there, not this matrix, the matrix I am talking about is this one. $$ A = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix} $$ Boring? But this is the fundamental thing that will connect you to “Neural Network” which is the building block of Artificial Intelligence and the like, surprisingly.