W3_L1: Introduction to vector spaces

Welcome to Week 3 Lecture 1 of the course "Mathematics for Data Science II" by Prof. Sarang S Sane. Full Course: https://study.iitm.ac.in/ds/course_pa... Video Overview This lecture marks the beginning of the study of vector spaces, one of the core topics in linear algebra. Professor Sarang Sane introduces the definition of a vector space and explains the essential properties that distinguish vector spaces from simple collections of vectors. Through examples from geometry and data analysis, the lecture illustrates how vectors can represent points, directions, and data features in multidimensional space. By the end of this session, learners will understand the basic structure, rules of addition and scalar multiplication, and the motivation for studying vector spaces as a foundation for advanced topics like linear transformations and eigenvalues. About IIT Madras' online Bachelor of Science programme IIT Madras offers four-year BS programmes that aim to provide quality education to all, irrespective of age, educational background, or location. The BS programme has multiple levels, which provide flexibility to students to exit at any of these levels. Depending on the courses completed and credits earned, the learner can receive a Foundation Certificate from IITM CODE (Centre for Outreach and Digital Education), Diploma(s) from IIT Madras, or BSc/BS Degrees from IIT Madras. For more details, visit: https://www.iitm.ac.in/academics/stud... #GaussianElimination #LinearEquations #SystemOfEquations #AugmentedMatrix #RowEchelonForm #ReducedRowEchelonForm #LinearAlgebra #Mathematics #Maths #Matrices #Determinant #InverseMatrix #HomogeneousEquations #SolvingEquations #Algorithms #Maths2 #VectorSpaces #DataScience #IITMadras #OnlineLearning