Principal Component Analysis (PCA) is a statistical method that has gained substantial importance in fields such as machine learning, data analysis, and signal processing. In essence, PCA is a dimensionality reduction technique that transforms large sets of variables into a smaller one, preserving as much of the original data’s variance as possible. Behind the curtains, …
Linear algebra, a branch of mathematics dealing with vectors and the rules for their operations, has many applications in the real world. One such application is in the field of machine learning, particularly in linear regression, a statistical method used to model the relationship between a dependent variable and one or more independent variables. In …
Linear algebra, often considered the cornerstone of advanced mathematics and foundational to multiple scientific fields, is primarily concerned with vector spaces and linear equations. One of its most fundamental concepts is the system of linear equations. Let’s delve into this topic to understand its significance and intricacies. What is a System of Linear Equations? At …
System of Equations – Understanding Linear Algebra System of Equations and Plotting Read More »
Introduction Singular Value Decomposition, commonly known as SVD, is a powerful mathematical tool in the world of data science and machine learning. SVD is primarily used for dimensionality reduction, information extraction, and noise reduction. In this post, we will delve deep into the world of SVD, understand its mechanics, and witness its applications with the …
Singular Value Decomposition – A Comprehensive guide on Singular Value Decomposition Read More »
The world of linear algebra is packed with fascinating concepts, and one of those is the affine transformation. If you’ve dabbled in computer graphics, image processing, or robotics, you’ve probably come across this term. Let’s dive deep into affine transformations, breaking them down and illustrating their applications with examples. What is an Affine Transformation? An …
Affine Transformation – A Comprehensive Guide on Affine Transformation in Linear Algebra Read More »
Eigenvectors and eigenvalues are fundamental concepts in linear algebra that have found applications in various domains, especially in data science. From Principal Component Analysis (PCA) to solving systems of differential equations, understanding these concepts is vital for anyone diving deep into the realm of data science. What are Eigenvectors and Eigenvalues? Let’s start with the …
Eigenvectors and Eigenvalues – Detailed Explanation on Eigenvectors and Eigenvalues Read More »
Welcome to a deep dive into the concepts of orthogonal and orthonormal second-order matrices. By the end of this blog post, you’ll understand what these terms mean, their significance in data science, and see them in action with some clear examples. Introduction In linear algebra and data science, the concept of orthogonality is fundamental. This …
Tensors, in general, are mathematical objects that generalize vectors, matrices, and higher-order structures, allowing us to describe more complex interactions, particularly in Data Science. A second-order tensor is often simply referred to as a matrix, but when discussing tensors, the context usually involves a broader mathematical or physical framework. Matrix or Second-Order Tensor A matrix …
Matrix theory is a fundamental aspect of linear algebra and plays a crucial role in a variety of scientific and engineering domains. While we often start with general matrices, certain types possess unique properties that make them essential in both theoretical and practical applications. In this post, we’ll delve into a handful of these special …
Matrix Types – Understanding Second Order Matrix Types with Examples Read More »
Vectors are a foundational concept in linear algebra and have broad applications across the sciences. Among the most fundamental ideas related to vectors are the concepts of basis, orthogonality, and orthonormality. Let’s take a closer look at each of these ideas with examples to deepen our understanding. Basis Vectors Orthogonal Vectors Orthonormal Vectors 1. Basis …
In the world of data science, vectors play a vital role. They are fundamental to machine learning, data analysis, and artificial intelligence. This post aims to break down the concepts of vectors, vector transposition, norms, and unit vectors, explaining their importance in the data science landscape. Vectors Vectors, also referred to as first-order tensors, are …
Vectors – Vector Transposition, Norms, and Unit Vectors: A Comprehensive Guide Read More »
What is a Scalar? A scalar is the simplest form of a tensor. It’s a single number, without direction. Scalars contrast with higher order tensors like vectors (1st order), matrices (2nd order), and so on. In other words, a scalar has zero dimensions. Why are Scalars Important? Foundation of Math Operations: When we work with …
Scalars – Understanding Scalars (Zero-Order Tensors) Read More »
Types of Tensors – A Comprehensive Guide in Exploring the Different Types of Tensors Introduction Tensors form the bedrock of many scientific disciplines, including physics, engineering, computer science, and specifically in the field of machine learning and artificial intelligence. Although often intimidating, they are merely a generalization of scalars, vectors, and matrices that can accommodate …
Types of Tensors – A Comprehensive Guide in Exploring the Different Types of Tensors Read More »
Let’s dive into the Core Concepts behind Linear Algebra with Examples & Illustrations. This is a series of lessons on Linear Algebra, covering the main ideas behind this important topics. Let’s get started. Introduction The world of data science is vast, complex, and intriguing. At the heart of many algorithms, especially in machine learning and …
