Vectors are linearly independent when no non-trivial linear combination of them equals the zero vector.
What Is Linear Independence?
Vectors are linearly independent when no non-trivial linear combination of them equals the zero vector.
Examples of Linear Independence
1
(1,0) and (0,1) are linearly independent.Formula and Key Points
Formula / rule
c₁v₁+…+cₙvₙ=0 ⇒ all cᵢ=0
- Know the definition and standard notation for Linear Independence.
- Be able to recognise or compute linear independence in a small example.
- Connect the concept to nearby topics in the same subject before using it in larger CSE problems.
Why This Matters in Computer Science
Used in computer graphics, machine learning, computer vision, signal processing, robotics and scientific computing.
Related Math Terms
Linear Independence: Frequently Asked Questions
What is Linear Independence?
Vectors are linearly independent when no non-trivial linear combination of them equals the zero vector.
Why is Linear Independence useful in computer science?
Used in computer graphics, machine learning, computer vision, signal processing, robotics and scientific computing.