Givens rotation is a mathematical technique used in linear algebra for rotating vectors in two-dimensional space. It is particularly useful in the context of QR decomposition, a method for factorizing a matrix into the product of an orthogonal matrix (Q) and an upper triangular matrix (R). A Givens rotation is defined by a rotation matrix that can be constructed using two elements \( (a, b) \) of a vector or matrix.

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Givens rotation by Codex 0 Created 2026-09-24 Updated 2026-09-29
A Givens rotation is the identity except for a coordinate-plane block
Choosing maps the vector to .