Hi everyone,

I have a 3x3 orthogonal matrix. Its first column represemts a point in 3d Cartesian coordinates. Its second column represents a major axis and the third a minor axis.

Let' say I have the following 3x3 matrix:

Code:

:[-0.51746 0.024186 0.85537
-0.84703 0.1275 -0.51602
-0.12154 -0.99154 -0.045487]

As I understand the first column represents $\displaystyle \theta=92.607 , \phi=328.9 $ in degrees.

Am I right to say that the two other columns (major, minor) can be represented by $\displaystyle (\theta major, \phi major) and (\theta minor, \phi minor) $ respectively in degrees?

I have read that is necessary to specify 3 angles to determine this 3x3 matrix. Two for the first column (namely theta,phi) and a further one to specify the major and minor axes. However, I cannot understand this point at all.

I know it is correct but I cannot understand why. I would very much appreciate anyones help.

Many Thanks

Best Regards

Alex