Vector Spaces Courses and Certifications

Tom Rocks Maths

Oxford Linear Algebra - Direct Sum of Vector Spaces

Learn how zero intersection makes a sum of subspaces direct, and test the definition with worked examples.

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

Tom Rocks Maths

Oxford Linear Algebra - Dimension Formula for Vector Spaces

A worked example in R⁴ motivates the dimension formula for subspaces, followed by a complete proof using a basis of their sum.

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

Vector Spaces

A proof-oriented introduction to vector spaces through subspaces, direct sums, dimension, replacement, and basis.

• YouTube
• 4 hours 30 minutes
• Self-Paced
• Free Video

Vector Spaces

Build an understanding of vector spaces through 25 examples, from subspaces and nullspaces to bases, coordinate changes, dimension, and infinite dimensions.

• YouTube
• 3 hours 30 minutes
• Self-Paced
• Free Video

Khan Academy

Linear Subspaces - Vectors and Spaces - Linear Algebra

Introduces linear subspaces of Rⁿ within a broader study of vectors and spaces in linear algebra.

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

Khan Academy

Linear Combinations and Span - Vectors and Spaces - Linear Algebra - Khan Academy

Understand how linear combinations generate the span of vectors in multidimensional spaces.

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

Vector Space - Linear Algebra

6 ratings

In this course, you will learn about Vector Space. These concepts are very important for Engineering and Basic Science students. This course is very useful for B.Sc./B.Tech students as well as for M.Sc./M.Tech. students who are preparing for NET, GATE an…

• YouTube
• 10 hours
• Self-Paced
• Free Video

Michael Penn

What Is the Free Vector Space?

An introduction to free vector spaces using a definition and examples.

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

Insights into Mathematics

Bases of Polynomial Spaces - Wild Linear Algebra - NJ Wildberger

Explore polynomial spaces through linear algebra, using bases, translations, and change-of-basis matrices to define derivatives algebraically.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Tom Rocks Maths

Oxford Linear Algebra - What is a Vector Space?

Axioms of vector spaces are tested on 3D coordinate vectors, with a proof that the additive identity is unique.

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

NPTEL-NOC IITM

Linear Independence - Lecture 2.1

Explore the concept of linear independence in vector spaces, understanding its significance and applications in linear algebra.

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

NPTEL-NOC IITM

Basics of Linear Algebra - Linear Independence

Explore linear independence, vector spaces, and basis concepts in linear algebra. Gain foundational knowledge for advanced mathematical applications.

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

Natural Language Processing with Classification and Vector Spaces

4647 ratings at Coursera

This is the Course 1 of the Natural Language Processing Specialization, offered by deeplearning.ai

• Coursera
• 4 weeks, 8 hours a week
• Self-Paced
• Paid Course

Insights into Mathematics

Change of Basis and Taylor Coefficient Vectors - Wild Linear Algebra A - NJ Wildberger

Explore change-of-basis matrices through coefficient vectors, Taylor bases, and generalized Pascal matrices.

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

Tom Rocks Maths

Oxford Linear Algebra - Inner Product Space

Defines inner product structures over real and complex vector spaces, then proves that every orthonormal set is linearly independent.

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