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- W4285653868 abstract "In this paper we derive closed form expressions for the nearest rank-(k) matrix on canonical subspaces. 
 
 We start by studying three kinds of subspaces. Let (X) and (Y) be a pair of given matrices. The first subspace contains all the (mtimes n) matrices (A) that satisfy (AX=O). The second subspace contains all the (m times n) matrices (A) that satisfy (Y^TA = O), while the matrices in the third subspace satisfy both (AX =O) and (Y^TA = 0).
 
 The second part of the paper considers a subspace that contains all the symmetric matrices (S) that satisfy (SX =O). In this case, in addition to the nearest rank-(k) matrix we also provide the nearest rank-(k) positive approximant on that subspace. 
 
 A further insight is gained by showing that the related cones of positive semidefinite matrices, and negative semidefinite matrices, constitute a polar decomposition of this subspace.
 The paper ends with two examples of applications. The first one regards the problem of computing the nearest rank-(k) centered matrix, and adds new insight into the PCA of a matrix.
 The second application comes from the field of Euclidean distance matrices. The new results on low-rank positive approximants are used to derive an explicit expression for the nearest source matrix. This opens a direct way for computing the related positions matrix." @default.
- W4285653868 created "2022-07-17" @default.
- W4285653868 creator A5009299181 @default.
- W4285653868 date "2020-09-08" @default.
- W4285653868 modified "2023-10-05" @default.
- W4285653868 title "Low-rank matrix approximations over canonical subspaces" @default.
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- W4285653868 doi "https://doi.org/10.33993/jnaat491-1195" @default.
- W4285653868 hasPublicationYear "2020" @default.
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