Modern hyperspectral images, especially acquired in remote sensing and from on‐field measurements, can easily contain from hundreds of thousands to several millions of pixels. This often leads to a quite long computational time when, eg, the images are decomposed by Principal Component Analysis (PCA) or similar algorithms. In this paper, we are going to show how random- ization can tackle this problem. The main idea is described in detail by Halko et al in 2011 and can be used for speeding up most of the low‐rank matrix decomposition methods. The paper explains this approach using visual interpretation of its main steps and shows how the use of randomness influences the speed and accuracy of PCA decomposition of hyperspectral images.