Further reading

Please find the additional reading content as follows:

• Householder reflection matrix: A Householder reflection matrix, or Householder matrix, is a type of linear transformation utilized in numerical linear algebra due to its computational effectiveness and numerical stability. This matrix is used to perform reflections of a given vector about a plane or hyperplane, transforming the vector so that it only has non-0 components in one specific dimension. The Householder matrix (H) is defined by

Here, I is the identity matrix, and u is a unit vector defining the reflection plane.

The main purpose of Householder transformations is to perform QR factorization and to reduce matrices to a tridiagonal or Hessenberg form. The properties of being symmetric and orthogonal make the Householder matrix computationally efficient and numerically stable.

• Diagonalizable: A matrix is said to be diagonalizable if it can be written in the form , where A is the...