(1 hours to learn)
The operations of the Gram-Schmidt procedure can be represented as a factorization of a matrix into an orthogonal matrix Q and an upper triangular matrix R. This is a useful representation for solving linear least squares problems.
This concept has the prerequisites:
- orthonormal bases (The Gram-Schmidt procedure is a simple algorithm for computing the QR decomposition.)
Core resources (read/watch one of the following)
→ MIT Open Courseware: Linear Algebra (2011)
Videos for an introductory linear algebra course focusing on numerical methods.
→ Introduction to Linear Algebra
An introductory linear algebra textbook with an emphasis on numerical methods.
Location: Section 4.4, "Orthogonal bases and Gram-Schmidt," subsection "The factorization A = QR," pages 235-238
- The Gram-Schmidt procedure is not numerically stable. In practice, we would compute the QR decomposition using one of:
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