Topic: Orthogonal Sets and Gram-Schmidt

Why Independent Inputs Give Nonzero Residuals

Why Gram-Schmidt Removes Earlier Components

The General Gram-Schmidt Recursion

Testing Orthogonality with Inner Products

Recovering Vectors from Orthonormal Coordinates

Pythagorean Identity for Orthogonal Sums

Proof That Gram-Schmidt Outputs Are Orthogonal

Proof That Gram-Schmidt Preserves Spans

Parseval’s Identity in Finite Dimensions

Orthonormal Coordinates in Function and Matrix Spaces