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- Title
Further results on tensor nuclear norms.
- Authors
Zeng, Chao
- Abstract
Several basic properties of tensor nuclear norms are established in [S. Friedland and L.-H. Lim, Math. Comp., 87 (2018), pp. 1255–1281]. In this work, we give further studies on tensor nuclear norms. We present some special cases of tensor nuclear decompositions. We list some examples to show basic relationships among tensor rank, orthogonal rank and nuclear rank. Spectral and nuclear norms of Hermitian tensors are studied. We show that spectral and nuclear norms of real Hermitian decomposable tensors do not depend on the choice of base field. At last, we extend matrix polar decompositions to the tensor case, which is the product of a Hermitian tensor and a tensor whose spectral norm equals one. That is, we establish a link between any tensor and a Hermitian tensor. Bounds of nuclear rank are given based on tensor polar decompositions.
- Subjects
TENSOR products; MATRIX decomposition; TRIANGULAR norms
- Publication
Calcolo, 2023, Vol 60, Issue 3, p1
- ISSN
0008-0624
- Publication type
Article
- DOI
10.1007/s10092-023-00528-2