0
$\begingroup$

The rotation transofrmation is defined as some composition of rotatation along the $x,y,z$ axes.

Assuming $T$ is a rotation transformation in $\mathbb{R}^{3}, v=\left(\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}\right), T\left(v\right)=\left(1,0,0\right)$

I need to find the matrix of $T$ according to the standard base. I was trying to find a rotation through $y$ axis such as $S_{\phi}\left(v\right)\subseteq XY$ plane, where $S$ is rotation along $y$-axis. Not sure if they meant $T$ is rotation along $z$-axis. But I am not sure if that's how I handle this question.

  • 0
    There seems to be insufficient information; also the vectors you have given us seems to be transposes of what you intended.2012-01-15
  • 3
    @KannappanSampath: I find your second remark a bit pedantic: certainly there is nothing wrong with denoting an element of $\mathbb R^3$ by a triplet of real numbers. The habit of writing them vertically helps us remember how to operate by a matrix on a vector, but I would not advocate imposing the use of distinct versions of $\mathbb R^3$ to contain column vectors and row vectors.2012-01-15

1 Answers 1