Mathematical Vectors

From fundamentals to advanced linear algebra. Learn vector operations, spaces, and their applications.

New to Vectors?

Start with the basics and work your way up to advanced topics.

Start with Vector Basics

1 Fundamentals

Vector Basics

What vectors are, notation, and basic properties

5 min read

Vector Magnitude

Calculating vector length and normalization

4 min read

Unit Vectors

Vectors of length 1 and their importance

4 min read

Vector Addition

Adding and subtracting vectors graphically and algebraically

5 min read

2 Operations

Dot Product

Popular

The scalar product and its geometric meaning

8 min read

Cross Product

3D vector multiplication and perpendicular vectors

7 min read

Vector Projection

Projecting one vector onto another

6 min read

3 Advanced Topics

Distance Metrics

Euclidean, Manhattan, Cosine, and more

8 min read

Vector Spaces

Abstract vector spaces and subspaces

10 min read

Linear Independence

Basis vectors and dimension

9 min read

Related Tools