**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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Householder notation is very simple:

Scalars are denoted as lowercase Greek letters: $\alpha$. $\beta$, $\gamma$, ...

Vectors are represented as lowercase English letters: $a$, $b$, $c$, ...

Matrices are denoted as uppercase English letters: $A$, $B$, $C$, ...

Vector transposes are denoted with the apostrophe ( ' )

Vector or matrix multiplication uses the star character ( * )

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

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

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

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

CC BY-SA 4.0 Jacob Zelko. Last modified: January 17, 2023.
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