This notebook builds the geometric and algebraic understanding of the determinant from first principles, culminating in why $\det(A) = 0$ is the exact condition for singularity. 1. The […]
How Non-Singular Matrices Act on Space
This notebook builds geometric intuition for matrix transformations, covering: 1. Active vs. Passive Interpretation Given a matrix $A$ and a vector $v$, the product $Av$ has two valid […]
Gradient Boosted Decision Trees (GBDT)
This notebook builds a complete understanding of GBDT from the ground up: 1. Decision Trees: The Weak Learner GBDT builds an ensemble of decision trees. Each tree partitions […]
Expected Prediction Error and the Regression Function
Source: Elements of Statistical Learning, Section 2.4 This notebook walks through the theoretical framework for supervised learning: why squared error loss is natural, what EPE is, and why […]
Derivation of the Least Squares Solution
This notebook derives the ordinary least squares (OLS) solution $\hat{x} = (A^\top A)^{-1} A^\top b$ from first principles using matrix algebra. 1. Problem Setup We want to solve […]
timeScale vs fixedDeltaTime
‘Time.timeScale‘ is a property in Unity that affects the scale at which time passes in the game. This property can be used to create effects such as slow […]
Difference between Gradient and Derivative
The concepts of ‘gradient’ and ‘derivate’ are fundamental in mathematics, particularly in calculus. Both relate to how functions change, but they apply in different contexts and have distinct […]
Fixed update with Physics.Simulate in Unity
When we set ‘Physics.simulationMode’ to ‘Script’, we can manually control the fixed update using ‘Physics.Simulate’. Here, we observe the differences when ‘Physics.simulationMode’ is placed at the top or […]
OpenMP and MPI
OpenMP(Open Multi-Processing) is an application programming interface (library) that supports multi-platform shared-memory parallel programming in C, C++ and Fortran on all architectures, including Unix and Windows platform. It […]
PRML Chapter 1
1.1 Example: Polynomial Curve Fitting Now suppose that we are given a training set comprising $N$ observations of $x$, written $\textbf{x} = (x_1, …, x_N)^{T}$ ,tother with corresponding […]