principal-components-analysis | Python/Numpy PCA using the transpose trick | Data Manipulation library

Two different methods of the principal component analysis were conducted to analyze the following data (ch082.dat) using the Box1's R-code, below.
https://drive.google.com/file/d/1xykl6ln-bUnXIs-jIA3n5S3XgHjQbkWB/view?usp=sharing

The first method uses the rotation matrix (See 'ans_mat' under the '#rotated data' of the Box1's code) and, the second method uses the 'pcomp' function (See 'rpca' under the '#rotated data' of the Box1's code).

However, there is a subtle discrepancy in the answer between the method using the rotation matrix and the method using the 'pcomp' function. make it match

My Question

What should I do so that the result of the rotation matrix -based method matches the result of the'pcomp' function?

As far as I've tried with various data, including other data, the actual discrepancies seem to be limited to scale shifts and mirroring transformations.

• The results of the rotation matrix -based method is shown in left panel.
• The results of the pcomp function -based method is shown in right panel.

Mirror inversion can be seen in "ch082.dat" data.(See Fig.1); It seems that, in some j, the sign of the "jth eigenvector of the correlation matrix" and the sign of the "jth column of the output value of the prcomp function" may be reversed. If there is a degree of overlap in the eigenvalues, it is possible that the difference may be more complex than mirror inversion.
Fig.1

There is a scale shift for the Box2's data (See See Fig.2), despite the centralization and normalization to the data.
Fig.2

Box.1