Material Detail

This resource introduces orthogonal projection in linear algebra and its geometric interpretation. A vector is decomposed into components parallel and perpendicular to a subspace, illustrating how projection identifies the closest point in that subspace.

Visual diagrams show the decomposition b = b∥ + b⊥, where b∥ lies in the subspace and b⊥ is orthogonal to it. The projection minimizes the distance between the vector and the subspace, providing a foundation for least squares and related methods.

The presentation connects algebraic formulas with geometric intuition and prepares students for topics such as QR factorization and linear regression.

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