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- W4308693300 abstract "We address the detection of a low rank $ntimes n$deterministic matrix $mathbf{X}_{0}$ from the noisy observation ${bf X}_{0}+{bf Z}$ when $ntoinfty$, where ${bf Z}$ is a complex Gaussian random matrix with independent identically distributed $mathcal{N}_{c}(0,frac{1}{n})$ entries. Thanks to large random matrix theory results, it is now well-known that if the largest singular value $lambda_{1}$ of ${bf X}_{0}$ verifies $lambda_{1}>1$, then it is possible to exhibit consistent tests. In this contribution, we prove a contrario that under the condition $lambda_{1}<1$, there are no consistent tests. Our proof is rather simple, inspired by previous works devoted to the case of rank 1 matrices ${bf X}_{0}$." @default.
- W4308693300 created "2022-11-14" @default.
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- W4308693300 date "2018-04-13" @default.
- W4308693300 modified "2023-09-28" @default.
- W4308693300 title "On the detection of low rank matrices in the high-dimensional regime" @default.
- W4308693300 doi "https://doi.org/10.48550/arxiv.1804.04851" @default.
- W4308693300 hasPublicationYear "2018" @default.
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