Reduction to Tridiagonal Form

Define a tridiagonal matrix and a Householder matrix, describing the latter's key properties (symmetry, orthogonality).

Construct a Householder matrix to zero out specified elements of a vector.

Perform the first iteration of Householder's method to reduce a symmetric 4x4 matrix, zeroing out the required elements in the first column.

Complete the tridiagonalization of the 4x4 matrix by performing the second and final iteration of Householder's method.