1. Home
  2. Material Detail: The Four Fundamental Subspaces of Linear Algebra

Material Detail

The Four Fundamental Subspaces of Linear Algebra

The Four Fundamental Subspaces of Linear Algebra

This resource introduces the four fundamental subspaces of linear algebra: column space, null space, row space and left null space.

The presentation explains the relationships between these spaces using visual tools. Diagrams and computational demonstrations connect algebraic procedures with their geometric meaning.

Keywords:
row reduction, left null space, four fundamental subspaces, null space, least squares, row space, column space, vector spaces, orthogonality, linear algebra, matrices
Disciplines:
Go to Material 
Bookmark / Add to Course ePortfolio
Create a Learning Exercise
Add Accessibility Information
Rate
Add a Comment

Quality

  • User Rating
  • Comments
  • Learning Exercises
  • Bookmark Collections
  • Course ePortfolios
  • Accessibility Info

More about this material

Material Type:
Reference Material
Date Added to MERLOT:
March 11, 2026
Date Modified in MERLOT:
March 11, 2026
Authors:
 
 
Submitter:
Eteri Byazrova
Primary Audience:
College Lower Division, College Upper Division
Technical Format:
PDF, Website
Mobile Compatibility:
Not specified at this time
Language:
English
Cost Involved:
No
Source Code Available:
No
Creative Commons:
Unknown

Browse...

Disciplines with similar materials as The Four Fundamental Subspaces of Linear Algebra
Other materials like The Four Fundamental Subspaces of Linear Algebra

Comments

Log in to participate in the discussions or sign up if you are not already a MERLOT member.