Householder Reflection
Chapter 4: QR Decomposition and Numerical Rank — Householder Reflection ($H$)
From the book
Chapter 4: QR Decomposition and Numerical Rank. In the chapter mind map this icon labels Householder Reflection ($H$). The discussion below is excerpted and lightly edited from § Householder Matrix and Householder Transformation in Mathematics for AI and Machine Learning.
The Householder transformation (also called Householder reflection) is a fundamental tool in numerical linear algebra for constructing orthonormal bases and performing QR decomposition. Unlike Gram–Schmidt, which builds orthonormal vectors incrementally, Householder transformations use geometric reflections to zero out matrix entries systematically.
What this drawing shows
What you see. Shows reflection-based orthogonal transformations used in QR factorization.
In the mind map. Chapter 4 — Householder Reflection (). See From the book above for definitions, figures, and worked examples.
Where to read next
Read the full definitions, figures, and worked examples in Chapter 4: QR Decomposition and Numerical Rank — see the mind-map node Householder Reflection ().
