Vector Spaces Courses and Certifications

NPTEL-NOC IITM

Vector Spaces: Introduction

Explore fundamental concepts of vector spaces, laying the groundwork for advanced linear algebra and mathematical analysis.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

Linear Combinations and Span - Introduction to Vector Spaces

Explore linear combinations and span concepts through intuitive explanations and graphical illustrations. Master fundamental linear algebra principles.

• YouTube
• 17 minutes
• Self-Paced
• Free Video

Wrath of Math

Isomorphic Vector Spaces and Isomorphisms - Linear Algebra

Explore isomorphic vector spaces and their properties, including examples and proofs. Learn how all n-dimensional spaces relate to R^n and understand key concepts in linear algebra.

• YouTube
• 17 minutes
• Self-Paced
• Free Video

Wrath of Math

General Linear Transformations on Vector Spaces

Explore general linear transformations on vector spaces, their properties, and examples. Learn to distinguish between linear and non-linear transformations in this comprehensive overview.

• YouTube
• 17 minutes
• Self-Paced
• Free Video

Linear Algebra: Matrix Algebra, Determinants, & Eigenvectors

79 ratings at Coursera

Manipulate matrices as compositions of linear transformations, test invertibility, identify subspaces and dimension in R^n, compute determinants, and diagonalize matrices using eigenvalues and eigenvectors.

• Coursera
• 6 weeks, 2 hours a week
• Self-Paced
• Paid Course

Land on Vector Spaces with Python

Explore linear algebra geometrically with Python, using transformations, eigenvalues, matrix decompositions, and singular-value decomposition in practical applications.

• Independent
• 4 weeks, 8 hours a week
• Self-Paced
• Free Online Course

Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra

Analyze complex variables, solve linear differential equations with Laplace transforms, and apply vector spaces, eigenvectors, determinants, and orthogonal functions.

• MIT OpenCourseWare
• Self-Paced
• Free Online Course

Wrath of Math

Elementary Linear Algebra - Complete Course

Master matrix operations, vector spaces, eigenvalues, and transformations through comprehensive lessons covering Gaussian elimination, determinants, orthogonality, and advanced topics.

• YouTube
• 17 hours 13 minutes
• Self-Paced
• Free Video

Tom Rocks Maths

Oxford Linear Algebra - Direct Sum of Vector Spaces

Comprehensive explanation of direct sum of vector spaces with worked examples. Learn formal definitions, alternative representations, and how to verify direct sums through intersection and spanning checks.

• YouTube
• 31 minutes
• Self-Paced
• Free Video

Michael Penn

The Vector Spaces for Vertex Algebras

Explore the infinite-dimensional vector spaces underlying vertex algebras through polynomial rings, exterior algebras, and Virasoro enveloping algebras.

• YouTube
• 21 minutes
• Self-Paced
• Free Video

Linear Algebra I: Vectors and Linear Equations

5 ratings at edX

This course provides an overview of bachelor-level linear algebra. You will review all the concepts and practice and refresh the skills related to vectors and linear equations.

• edX
• 6 weeks, 4-6 hours a week
• Self-Paced
• Free Online Course (Audit)

The Julia Programming Language

Ferrite.jl - True Vector Interpolations for H(div) and H(curl) Spaces

Discover how Ferrite.jl now supports H(div) and H(curl) vector interpolations for advanced finite element problems in electromagnetic and fluid dynamics applications.

• YouTube
• 19 minutes
• Self-Paced
• Free Video

矩阵分析（英文版）

introduce the key mathematical ideas in matrix theory, which are used in modern methods of matrix Lie groups, functional analysis, data analysis, scientific computing, optimization, and merely all quantitative fields of sci-ence and engineering.

• XuetangX
• Self-Paced
• Free Online Course

IIT Kharagpur;  NPTEL

Matrix Solver

Learn direct and iterative algorithms for efficiently solving large matrix equations, with mathematical foundations, convergence analysis, and working implementations.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

Matrix Calculus for Machine Learning and Beyond - IAP 2023

Master matrix calculus for machine learning with MIT's comprehensive approach to derivatives in higher dimensions, optimization, and automatic differentiation techniques.

• YouTube
• 13 hours 55 minutes
• Self-Paced
• Free Video