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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
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Properties & Relations  
Possible Issues  
Related Guides
Cite this Page
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:
  • ulinput stringupper/lower triangular string
    αinput expressionscalar mutliple
    xinput expressionvector
    ainput/output symbolmatrix; 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

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Basic Examples  (1)

Load the BLAS package:

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_2025_syr, author="Wolfram Research", title="{SYR}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/SYR.html}", note=[Accessed: 14-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_syr, organization={Wolfram Research}, title={SYR}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/SYR.html}, note=[Accessed: 14-August-2025]}