# Givens rotations versus Euler angles

#### makc

Trying to implement QR decomposition using Givens rotations, I calculate G1 to zero n32 of original matrix A, then G2 to zero n31 of G1 * A, then G2 to zero n21 of G2 * G1 * A. Residual matrix, R = G3 * G2 * G1 * A comes upper triangular as expected, so I believe my code is correct.

Looking at rotation matrix Q = G1^T * G2^T * G3^T against Euler rotation matrix X * Y * Z, I thought that I could use angles of Givens rotations as Euler angles up to sign correction at max.

To test this idea, I ran QR decomposition on pure rotation matrix A, expecting R to be identity matrix. This really worked out for certain rotataions, but for other cases, R was non-diagonal and, as you guessed, Givens rotations were nowhere near Euler angles.

I wonder where is a flaw could be in my idea or implementation?

Related Linear and Abstract Algebra News on Phys.org

#### fresh_42

Mentor
2018 Award
$Q^{-1}=(G_1\cdot G_2 \cdot G_3)^{-1} = G_3^{-1}\cdot G_2^{-1} \cdot G_1^{-1} \neq G_1^\tau\cdot G_2^\tau \cdot G_3^\tau$

"Givens rotations versus Euler angles"

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