The nuclear norm of a matrix is defined as the sum of its singular values, and it serves as a measure of matrix size that captures both the rank and the structure of the matrix. This norm is particularly important in various applications, such as low-rank approximation and optimization problems, where one seeks to minimize the nuclear norm to encourage sparsity in the singular value decomposition. The nuclear norm is a convex function, making it easier to optimize compared to other norms.
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