TRSM[sd,ul,ts,dg,α,a,b]
solves triangular systems of linear equations opts[a].x=α b or x.opts[a]==α b and resets b to the results x.
TRSM
TRSM[sd,ul,ts,dg,α,a,b]
solves triangular systems of linear equations opts[a].x=α b or x.opts[a]==α b and resets b to the results x.
Details and Options
- To use TRSM, you first need to load the BLAS Package using Needs ["LinearAlgebra`BLAS`"].
- The following arguments must be given:
-
sd input string left/right side stringul
- input string
upper/lower triangular stringts input string transposition stringdg input string diagonal ones stringα input expression scalar mutliplea input expression rectangular matrixb input/output symbol rectangular matrix; the symbol value is modified in place - The left/right side string sd may be specified as:
-
"L" a is on the left side of the dot product"R" a is on the right side of the dot product
- 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
- The transposition strings describe the operators opts and may be specified as:
-
"N" no transposition"T" transpose"C" conjugate transpose
- The diagonal ones string dg may be specified as:
-
"U" the main diagonal of a is assumed to contain only ones"N" the actual values of the main diagonal of a are used
- Dimensions of the matrix arguments must be such that the dot product is well defined.
Examples
open all close allBasic Examples (1)
Load the BLAS package:
Compute Inverse [UpperTriangularize [a]].b and save it in b:
Scope (4)
Real matrices:
Complex matrices:
Arbitrary-precision matrices:
Symbolic matrices:
Properties & Relations (4)
For invertible matrices a, TRSM["L","U","N","N",α,a,b] is equivalent to b=α Inverse [UpperTriangularize [a]].b:
For invertible matrices a, TRSM["L","L","T","N",α,a,b] is equivalent to b=α Inverse [Transpose [LowerTriangularize [a]]].b:
Note this is not TRSM["L","U","T","N",α,a,L] as the lower triangular part is used for the transpose:
If dg="U", the diagonal values of a are assumed to be ones:
The diagonal in a has been effectively replaced by ones:
If a is a rectangular matrix then only the leading upper or lower triangular part of a is used:
The matrix a is effectively truncated to its upper left corner:
Possible Issues (2)
The last argument must be a symbol:
The last argument must be initialized to a matrix:
Related Guides
Text
Wolfram Research (2017), TRSM, Wolfram Language function, https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/TRSM.html.
CMS
Wolfram Language. 2017. "TRSM." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/TRSM.html.
APA
Wolfram Language. (2017). TRSM. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/TRSM.html
BibTeX
@misc{reference.wolfram_2025_trsm, author="Wolfram Research", title="{TRSM}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/TRSM.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_trsm, organization={Wolfram Research}, title={TRSM}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/TRSM.html}, note=[Accessed: 17-November-2025]}