Linear Algebra › Section F · Orthogonality and least squares › Topic F.2
Orthogonal sets and complements
When the vectors of a basis meet at right angles, finding coordinates stops needing row reduction: each weight comes from one quick division. This topic shows why, meets the matrices whose columns behave this way, and describes everything perpendicular to a subspace.
In this topic
- Why right angles save work
- Orthogonal sets are independent
- Coordinates in an orthogonal basis
- Worked example: coordinates without row reduction
- Orthonormal sets and the test UᵀU = I
- Orthogonal matrices
- Orthogonal complements
- The row space, column space and null space
- Worked example: a basis for a complement
- Common mistakes to avoid
- Key takeaways
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