Householder Matrix

Author

Eric W. Weisstein
August 26, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/LinearAlgebra/HouseholderMatrix.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/HouseholderMatrix.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Code

HouseholderMatrix[v_?VectorQ]:=IdentityMatrix[Length[v]]-2 Transpose[{v}].{v}/(v.v)

Examples

HouseholderMatrix[Array[v,1]]//MatrixForm

HouseholderMatrix[Array[v,2]]//MatrixForm

HouseholderMatrix[Array[v,3]]//MatrixForm