givens_matrix

givens_matrix(a, b)

Compute the Givens rotation to zero out a row entry.

Returns a \(2 \times 2\) unitary matrix G that satisfies

\[\begin{split}G \begin{pmatrix} a \\ b \end{pmatrix} = \begin{pmatrix} r \\ 0 \end{pmatrix}\end{split}\]

where \(r\) is a complex number.

References

• https://en.wikipedia.org/wiki/Givens_rotation#Stable_calculation

• https://www.netlib.org/lapack/lawnspdf/lawn148.pdf

Parameters:

• a (complex) – A complex number representing the first row entry

• b (complex) – A complex number representing the second row entry

Returns:

The Givens rotation matrix.

Return type:

ndarray