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Advanced Proof

Finite Termination of Conjugate Gradient Method for Quadratic Functions

Students frequently conflate 'conjugacy' with 'orthogonality.' While orthogonal vectors satisfy piTpj=0 p_i^T p_j = 0 , conjugate vectors satisfy piTApj=0 p_i^T A p_j = 0 . Without the A A matrix in the inner product, the directions would not adapt to the specific curvature of the quadratic surface.
Institutional Reference: Fundamentals of Optimization
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