In SPSS, the syntax can help you to compute principal component score. If you want to use correlation matrix, please transform your observations to zscore in SPSS first.
MATRIX.
GET X/VARIABLES=X1 to Xp/MISSING=OMIT.
COMPUTE NR =NROW(X).
COMPUTE NC =NCOL(X).
COMPUTE XX1=SSCP(X).
COMPUTE XX2=CSUM(X).
COMPUTE XX3=XX2/NR.
COMPUTE SIGMA=(XX1-T(XX3)*XX3*NR)/(NR-1).
COMPUTE SDIAG=MAKE(NC,NC,0).
LOOP J=1 TO NC.
COMPUTE SDIAG(J,J)=1/SQRT(SIGMA(J,J)).
END LOOP.
COMPUTE CORR=SDIAG*SIGMA*SDIAG.
PRINT SIGMA.
PRINT SDIAG.
PRINT CORR.
CALL EIGEN(SIGMA,V,LAMBDA).
PRINT LAMBDA.
PRINT V.
COMPUTE VV=T(V)*V.
PRINT VV.
COMPUTE PSCORE=X*V.
SAVE PSCORE /OUTFILE=*.
END MATRIX.
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