Orthogonal sets
Intros
Lessons
- Orthogonal Sets and Basis
• Each pair of vector is orthogonal
• Linear independent → Form a Basis
• Calculate weights with Formula - Orthonormal Sets and Basis
• Is an orthogonal set
• Each vector is a unit vector
• Linear independent → Form a Basis - Matrix with Orthonormal columns and Properties
•
• 3 Properties of Matrix - Orthogonal Projection and Component
• Orthogonal Projection of onto
• The component of orthogonal to
Examples
Lessons
- Orthogonal Sets and Basis
Is this an orthogonal set?
- Verify that is an orthogonal basis for , and then express as a linear combination of the set of vectors in .
- Orthonormal Sets/Basis
Is set is an orthonormal basis for ? - Let where has orthonormal columns and . Verify that
- Orthogonal Projection
Let and . Write as the sum of two orthogonal vectors, one in Span{} and one orthogonal to .