Fourth order tensors and covariance tensors
- Resource Type
- Original Paper
- Authors
- Bai, Jinxuan; Wang, Jun; Xu, Changqing
- Source
- Annals of Functional Analysis. 14(3)
- Subject
- Fourth-order tensor
High order moment
Random matrix
Covariance tensor
53A45
15A69
- Language
- English
- ISSN
- 2639-7390
2008-8752
In this paper, we investigate the invertibility of the fourth-order cubic tensors and present several necessary and sufficient conditions for such tensors to be invertible. We also introduce tensors in statistics and use the fourth-order tensors to simplify the expressions of the higher order derivatives of a multivariate function. Finally, we define the covariance tensor of a random matrix X as a fourth-order tensor D[X]D[X] and show that D[X]D[X] is positive definite if X is square symmetric.