Dot Products, Orthogonality, and Projections
Measuring Angles, Length, and Finding the Closest Vector
Build a complete theory of measurement in linear algebra — dot products, lengths, angles, and orthogonality — then use orthogonal projection to solve the best approximation problem.
Sections
The Dot Product
10 min · 3 quiz questions · Interactive diagram
Length and Distance
8 min · 2 quiz questions
Angles and Orthogonality
10 min · 2 quiz questions · Interactive diagram
The Pythagorean Theorem
7 min · 2 quiz questions
Orthogonal Complement
10 min · 2 quiz questions
Orthonormal Sets and Matrices
10 min · 2 quiz questions
Weight Finding in an Orthonormal Basis
8 min · 2 quiz questions
Orthogonal Projection
12 min · 3 quiz questions · Interactive diagram
Best Approximation and Orthogonal Matrices
10 min · 3 quiz questions · Interactive diagram