LinearAlgebra`BLAS`
LinearAlgebra`BLAS`

# SYR

SYR[ul,α,x,a]

computes the symmetric rank-one update a+α Outer[Times,x,x] and resets the appropriate part of a to the result.

# Details and Options

• To use SYR, you first need to load the BLAS Package using Needs["LinearAlgebra`BLAS`"].
• The following arguments must be given:
•  ul input string upper/lower triangular string α input expression scalar mutliple x input expression vector a input/output symbol matrix; the symbol value is modified in place
• The upper/lower triangular string ul may be specified as:
•  "U" update the upper triangular part of a "L" update the lower triangular part of a
• 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 a symmetric rank-one update to the upper triangular part of 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)

SYR["U",α,x,a] is equivalent to a=a+α Outer[Times,x,x] for the upper triangular part of a:

The strictly lower triangular part of a is unchanged:

## Possible Issues(2)

The last argument must be a symbol:

The last argument must be initialized to a matrix:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2022_syr, author="Wolfram Research", title="{SYR}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/SYR.html}", note=[Accessed: 10-June-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_syr, organization={Wolfram Research}, title={SYR}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/SYR.html}, note=[Accessed: 10-June-2023 ]}