Using singular value decomposition to analyze drug/β-cyclodextrin mixtures: insights from X-ray powder diffraction patterns.The article discusses the use of mathematical models and linear algebra to understand the crystalline structures and interconversion pathways of drug complexes with β-cyclodextrin (β-CD).  Singular value decomposition (SVD) analysis is used to identify the presence of different polymorphs in the mixtures of these drugs and β-CD, determine interconversion pathways, and distinguish between different forms. 
Singular value decomposition
It involved the preparation and analysis of mixtures of indomethacin, diclofenac, famotidine, and cimetidine with β-CD using techniques such as differential scanning calorimetry (DSC), X-ray powder diffraction (XRPD), and proton nuclear magnetic resonance (1H-NMR). 
Differential scanning calorimetry (DSC)
It involved the preparation and analysis of mixtures of indomethacin, diclofenac, famotidine, and cimetidine with β-CD using techniques such as differential scanning calorimetry (DSC), X-ray powder diffraction (XRPD), and proton nuclear magnetic resonance (1H-NMR). 
X-ray powder diffraction (XRPD)
It involved the preparation and analysis of mixtures of indomethacin, diclofenac, famotidine, and cimetidine with β-CD using techniques such as differential scanning calorimetry (DSC), X-ray powder diffraction (XRPD), and proton nuclear magnetic resonance (1H-NMR). 
Proton nuclear magnetic resonance (1H-NMR)