Foundations
What is a Vector?
Introduction to vectors as arrows and lists of numbers.
Requirements:
Basic Algebra
Difficulty:
1
Vector Addition
How to add vectors geometrically and algebraically.
Requirements:
Vectors
Difficulty:
1
Scalar Multiplication & Unit Vectors
Scaling vectors and the concept of "unit vectors"
Requirements:
Vectors
Difficulty:
1
Linear Combinations
The fundamental building block of linear algebra.
Requirements:
Vectors
Difficulty:
2
What is Span?
Understanding the space reachable by a set of vectors.
Requirements:
Linear Combinations
Difficulty:
2
Linear Independence
Why some vectors are "redundant" in a set.
Requirements:
Span
Difficulty:
2
Basis of a Vector Space
The set of vectors that perfectly describe a space.
Requirements:
Independence
Difficulty:
3
Dimension Explained
Why we call a line 1D and a plane 2D.
Requirements:
Basis
Difficulty:
2
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