A Householder transformation, or Householder reflection, or Household matrix, is a reflection about a hyperplane with a unit normal vector. Not only have the Household matrices been used in QR decomposition efficiently but also implicitly and successfully applied in other areas. In the process of investigating a family of unitary filterbanks, a new family of Householder matrices are established. These matrices are produced when a matrix filter is required to preserve certain order of 2d digital polynomial signals. Naturally, they can be applied to image and signal processing among others.
A Family of Householder Matrices,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 16,
1, Article 11.
Available at: https://digitalcommons.pvamu.edu/aam/vol16/iss1/11