i acquired waveshare's (uart capacitive) fingerprint scanner which provides me with eigenvalues of a finger. these values are used to compare/classify fingerprints as per the scanners documentation. Fingerprint algorithms generally use PCA (principle component analysis) to get eigenvectors which are used for comparisons as per :
Principal Component Analysis for Minutiae Verification on Fingerprint Image (HSIEH,SHYU) &
Reconstruction of Fingerprints from Minutiae Points (Jidnya A. Shah)
Eigenvectors can be obtained from the eigenvalues if the original matrix A is given which we dont have as per the following equation.
(A - $\lambda$I)x = 0 where x is the eigenvector and $\lambda$ is the eigenvalue
And we know from studying the scanner that eigenvalues can either be used to directly match samples of fingerprint or there is a way to convert eigenvalues to eigenvector.
We already used Euclidean distance to directly compare eigenvalues of sample fingerprints. this resulted in results which were incorrect i.e. false samples getting matched etc.
What is the way therefore to use eigenvalues for classification?
I'm not sure how this is possible. One is a scalar, the other is a vector. An eigenvalue can correspond to a particular eigenvector via depending on the system matrix.
Usually PCA is used for dimensionality reduction, not really to "get" eigenvectors. You find principal directions, which are eignvectors of the covariance matrix of your data, and then you project the data down onto your principal vector directions.
The links you provided simply show how to find some optimal representation in a lower dimension to best represent your fingerprint data.
As for classification, I dont' know enough of your domain, but based on some references just read, it seems you would need more than just a Euclidean distance between eigenvalues for a consistently good classifier.