Givens Rotations

Orthogonal transformations via planar rotations

Algorithm

We apply a sequence of planar rotations $G(i,j,\theta)$ . Each rotation acts on two rows of the matrix simultaneously to introduce a single zero below the diagonal, gradually transforming $A$ into an upper triangular matrix $R$ .

Step-by-Step Transform

Step 0 of 6

StartFinish

Initial matrix

A

. The columns are shown as vectors.

Matrix Evolution

A \rightarrow \begin{bmatrix} 1.00 & 1.00 & 0.00 \\[0.5em] 1.00 & 2.00 & 1.00 \\[0.5em] 1.00 & 0.00 & 2.00 \end{bmatrix}

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