In this section, we introduced t-SVD and further define the tensor nuclear norm, tensor tubal rank, and tensor average rank. Based on these definitions, we analyze the solution to the TPCA problem. We also discuss the relations among the tensor rank in this section and other kinds of tensor...
Recently, theregularization based on t-SVD has been widely used in various low tubal-rank tensor recovery tasks. However, these models usually require smooth change of data along the third dimension to ensure their low rank structures. In this paper, we propose a new definition of data dependen...
The multiplication operator has an important interpretation in quantum mechanics. The adjoint operator may also be defined for unbounded linear operators with dense domains. Given a linear operator T: D(T) ⊂ H1 → H2 with dense domain D(T), let D(T*) be the subspace of all vectors y ...
Fourth-Rank Tensors of the Thirty-Two Crystal Classes: Multiplication Tables The fourth-rank tensors that embody the elastic or other properties of crystalline anisotropic substances can be partitioned into a number of sets in order... LJ Walpole - 《Proceedings of the Royal Society A ...
Fourth-Rank Tensors of the Thirty-Two Crystal Classes: Multiplication Tables The fourth-rank tensors that embody the elastic or other properties of crystalline anisotropic substances can be partitioned into a number of sets in order... LJ Walpole - 《Proceedings of the Royal Society A Mathematica...
Tensor rank is NP-complete Abstract We prove that computing the rank of a three-dimensional tensor over any finite field is NP-complete. Over the rational numbers the problem is NP-hard.
示例3: clip_tensor ▲点赞 6▼ # 需要导入模块: import tensorflow [as 别名]# 或者: from tensorflow importrank[as 别名]defclip_tensor(t, length):"""Clips the input tensor along the first dimension up to the length. Args: t: the input tensor, assuming therankis at least 1. ...
This note is concerned with properties of the~tensor rank that is a natural generalization of the matrix rank. The topological group structure of invertible matrices is involved in this study. The multilinear matrix multiplication is discussed from a viewpoint of transformation groups. We treat a ...
S. Ballet. On the tensor rank of the multiplication in the finite fields. Journal of Number Theory, 128:1795-1806, 2008.S. Ballet. On the tensor rank of the multiplication in the finite fields. Journal of Number Theory 128, 6, 1795-1806, 2008....
\({{\mathrm{rank}}}_+ m_n \le n^3\) . it turns out that this is actually tight as one can show that \(\tau _+(m_n) = n^3\) . proposition 5 let \(m_n\) be the \(n^2 \times n^2 \times n^2\) matrix multiplication tensor defined in ( 37 ). then \(\tau _+...