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Jun 20, 2015 at 1:33 comment added user32398 As long as the matrix is not singular and none of the eigenvalues are zero, most algorithm results should be the same, except for a 180 degree change in the signs - which is not guaranteed.
Jun 18, 2015 at 0:32 comment added Anonymous @LEP : I faced the same problem with inversion, maybe you have already found solution for this issue - how to find out that first vector is correct and make sure that the rest will be aligned to it properly - quant.stackexchange.com/questions/3094/… ?
Jan 29, 2014 at 12:47 comment added user32398 Correct, the sign of loadings doesn't matter (orientation). Something that was not addressed was that if you perform this across different software packages, the between-package differences is that one program may result in negative(positive) signs on particular loadings while another results in positive(negative) signs for the same loadings. Therefore, the signs of the final results in the 3-series plot above could be inverted when using another package. The reference vector loadings could also have a sign change - and this solution would not be incorrect.
Aug 16, 2012 at 0:17 comment added David J. Harris @whuber Nice work.
Aug 15, 2012 at 21:57 comment added whuber Good idea. I tried this first (probably while you were posting this answer :-). The problem is that the other loadings can jump around. To fix this, base the sign choice on the largest loading. Still no dice: the loadings can still jump. The trick is at each time to choose the orientation that creates the least disturbance in the vector of loadings from the previous time.
Aug 15, 2012 at 20:58 history edited David J. Harris CC BY-SA 3.0
change "value" to "vector" in the first sentence for clarity
Aug 15, 2012 at 20:45 history answered David J. Harris CC BY-SA 3.0