SYMV[ul,α,a,x,β,y]
computes the symmetric matrix-vector multiplication α a.x+β y and resets y to the result.
SYMV
SYMV[ul,α,a,x,β,y]
computes the symmetric matrix-vector multiplication α a.x+β y and resets y to the result.
Details and Options
- To use SYMV, you first need to load the BLAS Package using Needs ["LinearAlgebra`BLAS`"].
- The following arguments must be given:
-
ul input string upper/lower triangular stringα input expression scalar mutliplea input expression square symmetric matrixx input expression vectorβ input expression scalar multipley input/output symbol vector; the symbol value is modified in place
- The matrix is assumed symmetric, and only the upper or lower triangular part of a is used.
- The upper/lower triangular string ul may be specified as:
-
"U" the upper triangular part of a is to be used"L" the lower triangular part of a is to be used
- Dimensions of the matrix and vector arguments must be such that the dot product and addition are well defined.
Examples
open all close allBasic Examples (1)
Load the BLAS package:
Compute a.x+2y and save it in y:
Scope (4)
Real symmetric matrix and vectors:
Complex symmetric matrix and vectors:
Arbitrary-precision symmetric matrix and vectors:
Symbolic symmetric matrix and vectors:
Properties & Relations (3)
SYMV["U",α,a,x,β,y] is equivalent to y=α a.x+β y if a is symmetric:
For a symmetric matrix, using the upper or lower triangular part generally produces the same result:
SYMV works with a non-symmetric matrices:
However, the upper and lower parts give different results:
The effective computation of yU is the following:
Possible Issues (2)
The last argument must be a symbol:
The last argument must be initialized to a vector:
Related Guides
Text
Wolfram Research (2017), SYMV, Wolfram Language function, https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/SYMV.html.
CMS
Wolfram Language. 2017. "SYMV." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/SYMV.html.
APA
Wolfram Language. (2017). SYMV. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/SYMV.html
BibTeX
@misc{reference.wolfram_2025_symv, author="Wolfram Research", title="{SYMV}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/SYMV.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_symv, organization={Wolfram Research}, title={SYMV}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/SYMV.html}, note=[Accessed: 17-November-2025]}