Student[LinearAlgebra]
HouseholderMatrix
construct a Householder Matrix
Calling Sequence
Parameters
Description
Examples
Compatibility
HouseholderMatrix(V, options)
V
-
Vector; used for constructing the Householder Matrix
options
(optional) parameters; for a complete list, see LinearAlgebra[HouseholderMatrix]
The HouseholderMatrix(V) function constructs a Householder Matrix from the values in the Vector V.
If V is a Vector of dimension n and V+ indicates its transpose, then HouseholderMatrix(V) constructs the Matrix Id−sV.V+ (if V is a column Vector) or Id−sV+.V (if V is a row Vector), where Id=IdentityMatrixn and s=2V.V by default. You can provide a different value for s. See LinearAlgebra[HouseholderMatrix] for more information.
withStudentLinearAlgebra:
V≔3,4,5
V≔345
NormV
52
W≔V+NormV·1,0,0
W≔3+5245
H≔HouseholderMatrixW
H≔1−23+52241+3+522−83+5241+3+522−103+5241+3+522−83+5241+3+5221−3241+3+522−4041+3+522−103+5241+3+522−4041+3+5221−5041+3+522
evalaH·V
−5200
The Student[LinearAlgebra][HouseholderMatrix] command was introduced in Maple 2016.
For more information on Maple 2016 changes, see Updates in Maple 2016.
See Also
Matrix
Vector
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