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The study of the properties of real and complex matrices that are more close to analysis and operator theory. For instance: the properties of positive definite matrices, matrix inequalities, perturbation analysis, matrix functions, inequalities between eigenvectors and singular values, majorization.

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Restricted Isometry Property for Discrete Fourier Transform Matrix

This is a solved problem, see for instance http://www.mathc.rwth-aachen.de/~rauhut/files/LinzRauhut.pdf . See for instance theorem 4.3 for non uniform recovery results. For more general estimations …
Jean-Luc Bouchot's user avatar