Gram-Schmidt & QR Factorization

University Projects #Mathematics#Data Science

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Overview#

Implementation of the Gram-Schmidt orthonormalization process and QR factorization from scratch in R. These fundamental linear algebra algorithms are essential for numerical computing, least squares problems, and eigenvalue computation.

Key Concepts#

Implemented Gram-Schmidt orthonormalization algorithm step by step
Built QR factorization using the orthonormalized vectors
Created validation tests comparing custom implementation to R’s built-in qr()
Documented mathematical proofs alongside code
Visualized orthonormal basis transformations