Maintaining multivariate calibrations involves keeping models developed on an instrument applicable to predicting new samples over time. Sometimes, a primary instrument model is needed to predict samples measured on secondary instruments. This situation is referred to as calibration transfer. Sometimes, a primary instrument model is needed to predict samples that have acquired new spectral features (chemical, physical, and environmental influences) over time. This situation is referred to as calibration maintenance. Calibration transfer and maintenance problems have a long history and are well studied in chemometrics and spectroscopy. In disciplines outside of chemometrics, particularly computer vision, calibration transfer and maintenance problems are more recent phenomena, and these problems often go under the umbrella term domain adaptation. Over the past decade, domain adaptation has demonstrated significant successes in various applications such as visual object recognition. Since domain adaptation already constitutes a large area of research in computer vision and machine learning, we narrow our scope and report on penalty-based eigendecompositions, a class of domain adaptation methods that has its motivational roots in linear discriminant analysis. We compare these approaches against chemometrics-based approaches using several benchmark chemometrics data sets. In disciplines outside of chemometrics, particularly computer vision, problems involving calibration updating, e.g., calibration transfer or maintenance, are more recent phenomena, and these problems often go under the umbrella term domain adaptation (DA). We report on penalty-based eigendecompositions, a class of DA methods that has its motivational roots in linear discriminant analysis. These DA methods are coopted for chemometrics-based purposes and are then compared with known calibration updating methods.