the cedar ledge

# Householder Notation

Date: June 3 2020

Summary: Summary of how Householder notation works

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

# Bibliography

Not Available

Householder notation is very simple:

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

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

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

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 $u' * v = \alpha$ (i.e. a transposed vector times a vector yields a scalar)

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

3. 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)

## How To Cite

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

## Discussion:

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