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In this answer, the Cholesky decomposition of a correlation matrix is suggested as the means for testing for multicollinearity.

I have a dataset that I am certain has high collinearity. I did the analysis and got results. Given adj as a correlation matrix for 151 features,

>>> np.diag(np.linalg.cholesky(adj))
array([ 1.        ,  0.81271258,  0.4347411 ,  0.35191732,  0.06531301,
        0.10419741,  0.36295611,  0.23152931,  0.19693139,  0.19316466,
        0.18088109,  0.09936057,  0.03281895,  0.49244854,  0.81039003,
        0.22115652,  0.33041865,  0.2780319 ,  0.25048447,  0.22880952,
        0.10268844,  0.11673899,  0.01344738,  0.56671684,  0.14804953,
        0.12409195,  0.21649726,  0.06802142,  0.07285222,  0.64329947,
        0.44850262,  0.54036702,  0.20295864,  0.30574657,  0.02818365,
        0.09465424,  0.23618057,  0.07895188,  0.11395146,  0.13379301,
        0.05233691,  0.03264139,  0.01233736,  0.16267169,  0.38258916,
        0.13865424,  0.10984987,  0.18904189,  0.085058  ,  0.08372508,
        0.03697817,  0.04518786,  0.00572868,  0.33820285,  0.04428341,
        0.04016906,  0.0664408 ,  0.02632276,  0.02387378,  0.36473254,
        0.52556407,  0.17516309,  0.1882489 ,  0.29015632,  0.02547512,
        0.05520855,  0.17017984,  0.03552853,  0.04676994,  0.04775287,
        0.0215077 ,  0.01259108,  0.00689978,  0.06105766,  0.16721513,
        0.03824157,  0.031524  ,  0.10582042,  0.02546902,  0.03537411,
        0.01663049,  0.02598288,  0.00217898,  0.11040083,  0.00942264,
        0.01061127,  0.02001356,  0.00976359,  0.00450101,  0.1154121 ,
        0.85058981,  0.93834185,  0.66425652,  0.45567434,  0.13514053,
        0.29548794,  0.87091404,  0.41733989,  0.45835938,  0.71899103,
        0.26597099,  0.24568093,  0.085093  ,  0.76427871,  0.72854252,
        0.49240519,  0.63656468,  0.71823761,  0.46800577,  0.54998874,
        0.20593099,  0.39427862,  0.04181777,  0.97416453,  0.20255577,
        0.33461707,  0.24953609,  0.22751523,  0.15212806,  0.93246527,
        0.92625935,  0.50125448,  0.62746354,  0.27962919,  0.22002931,
        0.1043165 ,  0.10673018,  0.33595362,  0.32514927,  0.15828758,
        0.40790439,  0.27769578,  0.14303885,  0.04538492,  0.47776144,
        0.50397431,  0.20470411,  0.38812498,  0.31299977,  0.25798637,
        0.247477  ,  0.08310196,  0.12468404,  0.02408655,  0.61922747,
        0.17409325,  0.29628727,  0.23251925,  0.09366473,  0.16396526,
        0.56806323])

Great. I have 151 numbers on the diagonal corresponding to 151 features. 49 are less than 0.1; 6 are less than 0.01.

What does this numerical information tell me? Can I associate the low numbers with features on the diagonal (since I have the order of rows and columns from the correlation matrix)? If I can associate them, does this tell me that certain features are highly collinear with at least one other feature?

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