Orthogonal Complement

A subspace perpendicular to another subspace. It is a Perpendicular Set, but for Subspaces

Definition

The orthogonal complement $W^{\perp }$ of a subspace $W\subset V$ is the subspace $W^{\perp }=\{v\in V|⟨v|w⟩=0,\forall w\in W\}$

Theorems

• Orthogonal Projection of Perpendicular Set Theorem
• Subspace and Orthogonal Complement for a Direct Sum
• Orthogonal Projection onto Orthogonal Complement
• Bessels Inequality

Implementaitons

• Perpendicular Set

Guides

• Finding Orthogonal Complement