Are PCA solutions unique?

When I run PCA on a certain data set, is the solution given to me unique?

I.e., I obtain a set of 2d coordinates, based on interpoint distances.
Is it possible to find at least one more arrangement of the points that would meet these constraints?

If the answer is yes, how can I find such different solution?

Answer

Something that hasn’t been noticed yet is that simply reversing the sign of a PC produces a different solution. That is, if \mathbf{w} is the nth principal component, then -\mathbf{w} is also a solution to the nth principal component. This has caused confusion before, especially when your computer outputs alternating PCs. See this question.

Attribution
Source : Link , Question Author : raygozag , Answer Author : Community

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