# solving a system of equation by rotation

Somebody hinted that one can solve a system of equations with some method of rotation. This is only needed for numeric solutions, otherwise Gauss-Jordan (RREF) is just fine.

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That would be either QR decomposition (which is doable with rotation matrices), or the eigendecomposition of a matrix with Jacobi's algorithm. Both are more expensive than Gaussian elimination, which remains applicable for numerical solutions as long as you pivot. –  Guess who it is. Sep 19 '11 at 16:21

Also, you have the convention backwards. $\mathbf Q$ is the orthogonal factor (it's supposed to be $\mathbf O$, but seeing that "O" often gets confused with "0"...) and $\mathbf R$ is the upper triangular (or "right triangular") factor. –  Guess who it is. Dec 27 '11 at 10:31