In this study we present a technique to embed a digital watermark containing copyright information into a spectral image. The watermark is embedded in a transform domain of the spectral dimension of the image. The transform domain is derived by performing the principal component analysis (PCA) transform on the original image. The watermark is embedded by modifying the coefficients of the eigenvectors from the PCA transform. After modification the image is reconstructed by the inverse PCA transform, thus containing the watermark. We provide analysis of watermark's imperceptibility and robustness against attacks with various parameter values in embedding and in attacks. The attacks include lossy image compression by the wavelet transform, median filtering and mean filtering. Experimental results indicate that the watermarked image is very similar to the original one and the watermark can be extracted with reasonable visual fidelity from the image after the attacks.