# Blog posts

## 2021

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This post is a quick note to myself regarding bias-variance trade-off. The note is compilation of Andrew Ng’s machine learning lecture and my understanding. I hope someone may find it insight full.

## Stability of Fixed Points of High Dimensional Dynamical Systems

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In the previous post, I discussed the basics regarding the stability of fixed points of a dynamical system and explained it with a simple continuous-time one-dimensional example. In this post, I will discuss fixed points for a general case of a continuous-time $n$-dimensional system.

## Notes on Vector Calculus

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This post contains some of the important notes which come in handy while working with vector-calculus.

## Rotation using Euler Angles

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I have always found rotation using Euler angles confusing. This post is just a simple note to maintain my sanity while performing rigid body transformations using Euler angles and rotational matrices.

## Stablility of Fixed Point of a Dynamical System

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Stability theory is used to address the stability of solutions of differential equations. A dynamical system can be represented by a differential equation. The stability of the trajectories of this system under perturbations of its initial conditions can also be addressed using the stability theory.

## Quaternion Rotation

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Quaternions are a number system that extends complex numbers. A quaternion provides a convenient mathematical notation for representing orientations and rotations of an object in three dimensions. This section discusses some of the useful properties and operations which are used in quaternion rotation.