I am using Matlab function PCA (principal component analysis) to reduce the dimensionality of a data set with approximately 20 000 observations x 100 dimensions.

After having obtained the principal component coefficients of the data I recreated the input signal in the original coordinate system using the transformation matrix from the PCA function. This yielded a very large residual when comparing with the input signal. I have tried around with different data sets and sizes and it appears to be commonplace to have a large residual. I am not sure yet whether it is due to round-off errors or high SNR in the input data. The dimensionality reduction could of course still be useful, but is this something that one should be cautious about when performing principal component analysis? Or is there another metric that is better to assess the performance of the principal component analysis?