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HERK[ul,ts,α,a,β,b]

computes the Hermitian rank-k update α opts[a].ConjugateTranspose[opts[a]]+β b and resets the appropriate part of b to the result.

更多信息和选项
Details and Options Details and Options
范例  
基本范例  
Scope  
Properties & Relations  
Possible Issues  
相关指南
按以下格式引用：
LinearAlgebra`BLAS`
LinearAlgebra`BLAS`

HERK

HERK[ul,ts,α,a,β,b]

computes the Hermitian rank-k update α opts[a].ConjugateTranspose[opts[a]]+β b and resets the appropriate part of b to the result.

更多信息和选项

  • To use HERK, you first need to load the BLAS Package using Needs["LinearAlgebra`BLAS`"].
  • The following arguments must be given:
  • ulinput stringupper/lower triangular string
    tsinput stringtransposition string
    αinput expressionscalar mutliple
    ainput expressionrectangular matrix
    βinput expressionscalar multiple
    binput/output symbolsquare 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 b
    "L"update the lower triangular part of b
  • The transposition strings describe the operators opts and may be specified as:
  • "N"no transposition
    "T"transpose
    "C"conjugate transpose
  • The main diagonal elements of b are assumed to be real-valued.
  • Dimensions of the matrix arguments must be such that the dot product and addition are well defined.

范例

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基本范例  (1)

Load the BLAS package:

Wolfram Language code: Needs["LinearAlgebra`BLAS`"]

Apply Hermitian rank-2 update to the upper triangular part of a matrix:

Wolfram Language code: b = {{2, 1 + I}, {1 - I, 3}}; a = {{I, 2 - I}, {3 + 2I, 4}}; HERK["U", "N", 1, a, 2, b]; b

Scope  (4)

Real matrices:

Wolfram Language code: b = {{1., 0., 0.}, {0., 1., 0.}, {0., 0., 1.}}; a = {{-2.1, 0., 3.2}, {4.3, 0.2, -0.3}, {4.1, 2.6, 0.}}; HERK["U", "T", 1., a, 2., b]; b

Complex matrices:

Wolfram Language code: b = {{2., 1. - I}, {1. + I, 3.}}; a = {{2.1 + 0.5I, 3.2 + I}, {4.1I, 3.8}}; HERK["L", "C", 1., a, -1., b]; b

Arbitrary-precision matrices:

Wolfram Language code: b = {{2`20, 1 + I}, {1 - I, 3}}; a = {{I, 2 - I}, {3 + 2I, 4}}; HERK["U", "N", 1, a, 2, b]; b

Integer-symbolic matrices:

Wolfram Language code: Clear[α, β] b = {{1, 0}, {0, 1}}; a = {{a11}, {a22}}; HERK["U", "N", α, a, β, b]; b

Properties & Relations  (1)

HERK["U","N",α,a,β,b] is equivalent to b=α a.ConjugateTranspose[a]+β b applied to the upper triangular part of b:

Wolfram Language code: b = RandomComplex[1 + I, {5, 5}]; b = b1 = (b + ConjugateTranspose[b]) / 2; a = RandomComplex[1 + I, {5, 3}]; α = RandomReal[]; β = RandomReal[]; HERK["U", "N", α, a, β, b]; UpperTriangularize[b] == UpperTriangularize[α a.ConjugateTranspose[a] + β b1]

The strictly lower triangular part of b is unchanged:

Wolfram Language code: LowerTriangularize[b, -1] == LowerTriangularize[b1, -1]

Possible Issues  (2)

The last argument must be a symbol:

Wolfram Language code: HERK["U", "N", 1 / 2, {{1, 2}, {-2, 1}}, 2, {{1, 2}, {3, 4}}]

The last argument must be initialized to a matrix, otherwise an error message is issued:

Wolfram Language code: Clear[b]; HERK["U", "N", 1 / 2, {{1, 2}, {-2, 1}}, 2, b]
Wolfram Research (2017)，HERK，Wolfram 语言函数，https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/HERK.html.

文本

Wolfram Research (2017)，HERK，Wolfram 语言函数，https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/HERK.html.

CMS

Wolfram 语言. 2017. "HERK." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/HERK.html.

APA

Wolfram 语言. (2017). HERK. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/HERK.html 年

BibTeX

@misc{reference.wolfram_2026_herk, author="Wolfram Research", title="{HERK}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/HERK.html}", note=[Accessed: 19-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_herk, organization={Wolfram Research}, title={HERK}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/HERK.html}, note=[Accessed: 19-August-2026]}