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Determining the intrinsic dimension of a hyperspectral image is an important step in the spectral unmixing process and under- or overestimation of this number may lead to incorrect unmixing in unsupervised methods. In this paper, we discuss a new method for determining the intrinsic dimension using recent advances in random matrix theory. This method is entirely unsupervised, free from any user-determined parameters and allows spectrally correlated noise in the data. Robustness tests are run on synthetic data, to determine how the results were affected by noise levels, noise variability, noise approximation, and spectral characteristics of the end-members. Success rates are determined for many different synthetic images, and the method is tested on two pairs of real images, namely a Cuprite scene taken from Airborne Visible InfraRed Imaging Spectrometer (AVIRIS) and SpecTIR sensors, and a Lunar Lakes scene taken from AVIRIS and Hyperion, with good results.