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

$$\begin{array}{r}G\left(\begin{array}{c}a\\ b\end{array}\right)=\left(\begin{array}{c}r\\ 0\end{array}\right)\end{array}$$

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