LinearAlgebra`BLAS`
LinearAlgebra`BLAS`

# GERC

GERC[α,x,y,a]

computes the rank-one update a+αOuter[Times,x,Conjugate[y]] and resets a to the result.

# Details and Options

• To use GERC, you first need to load the BLAS Package using Needs["LinearAlgebra`BLAS`"].
• The following arguments must be given:
•  α input expression scalar mutliple x input expression vector y input expression vector a input/output symbol matrix; the symbol value is modified in place
• Dimensions of the matrix and vector arguments must be such that the dot product and addition are well defined.

# Examples

open allclose all

## Basic Examples(1)

Apply rank-one update to a matrix:

## Scope(4)

Real matrix and vectors:

Complex matrix and vectors:

Arbitrary-precision matrix and vectors:

Integer-symbolic matrix and vectors:

## Properties & Relations(1)

• GERC[α,x,y,a] is equivalent to a=a+αOuter[Times,x,Conjugate[y]]:
• This can also be expressed as a=a+αTranspose[{x}].{Conjugate[y]}:

## Possible Issues(2)

The last argument must be a symbol:

The last argument must be initialized to a matrix:

Wolfram Research (2017), GERC, Wolfram Language function, https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GERC.html.

#### Text

Wolfram Research (2017), GERC, Wolfram Language function, https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GERC.html.

#### CMS

Wolfram Language. 2017. "GERC." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GERC.html.

#### APA

Wolfram Language. (2017). GERC. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GERC.html

#### BibTeX

@misc{reference.wolfram_2023_gerc, author="Wolfram Research", title="{GERC}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GERC.html}", note=[Accessed: 20-May-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2023_gerc, organization={Wolfram Research}, title={GERC}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GERC.html}, note=[Accessed: 20-May-2024 ]}