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Householder Notation

Date: June 3 2020

Summary: Summary of how Householder notation works

Keywords: ##zettel #linear #algebra #matrix #vector #scalar #greek #householder #notation #archive

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Table of Contents

    1. Examples
  1. How To Cite
  2. References
  3. Discussion:

Householder notation is very simple:

  1. Scalars are denoted as lowercase Greek letters: α\alpha. β\beta, γ\gamma, ...

  2. Vectors are represented as lowercase English letters: aa, bb, cc, ...

  3. Matrices are denoted as uppercase English letters: AA, BB, CC, ...

  4. Vector transposes are denoted with the apostrophe ( ' )

  5. Vector or matrix multiplication uses the star character ( * )

Examples

  1. The inner product can be expressed as uv=αu' * v = \alpha (i.e. a transposed vector times a vector yields a scalar)

  2. The outer product can be expressed similarly as uv=Au * v' = A (i.e. a vector times a transposed vector yields a matrix)

  3. Quadratic/bilinear forms can be written as uAv=βu' * A * v = \beta (i.e. a transposed vector times a matrix times a vector yields a scalar)

How To Cite

Zelko, Jacob. Householder Notation. https://jacobzelko.com/06032020153234-householder-notation. June 3 2020.

References

Discussion:

CC BY-SA 4.0 Jacob Zelko. Last modified: January 17, 2023. Website built with Franklin.jl and the Julia programming language.