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The CUR matrix approximation is often {{citation needed|date=November 2012}} used in place of the low-rank approximation of the SVD in [[principal component analysis]]. The CUR is less accurate, but the columns of the matrix ''C'' are taken from ''A'' and the rows of ''R'' are taken from ''A''. In PCA, each column of ''A'' contains a data sample; thus, the matrix ''C'' is made of a subset of data samples. This is much easier to interpret than the SVD's left singular vectors, which represent the data in a rotated space. Similarly, the matrix ''R'' is made of a subset of variables measured for each data sample. This is easier to comprehend than the SVD's right singular vectors, which are another rotations of the data in space.
==Matrix CUR==
Hamm<ref>Keaton Hamm and Longxiu Huang. Perspectives on CUR decompositions. Applied and Computational Harmonic Analysis, 48(3):1088–1099, 2020.</ref> and Aldroubi et al.<ref>Aldroubi, Akram and Hamm, Keaton and Koku, Ahmet Bugra and Sekmen, Ali. CUR decompositions, similarity matrices, and subspace clustering. Frontiers in Applied Mathematics and Statistics, 2019, Frontiers Media SA</ref> describe the following theorem, which outlines a CUR decomposition of a matrix <math>L</math> with rank <math>r</math>:
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