Tensor and Covariance Matrices

Wei Lan and Chih-Ling Tsai
Additional contact information
Wei Lan: Southwestern University of Finance and Economics, School of Statistics and Data Science and Center of Statistical Research
Chih-Ling Tsai: University of California - Davis, Graduate School of Management

Chapter Chapter 10 in Covariance Analysis and Beyond, 2026, pp 183-202 from Springer

Abstract: Abstract This chapter briefly reviews tensor operations and then focuses on tensor covariances; it consists of four sections. Section 10.1 presents two tensor operations that are tensor products and decompositions. To analyze linear relationships between two tensors (i.e., multi-arrays), Sect. 10.2 introduces tensor covariance, tensor correlation, and tensor canonical correlationTensor canonical correlation. Subsequently, Sect. 10.3 studies three types of tensor covariance modelsTensor covariance models, which are the separable covariance modelSeparable covariance model, the core shrinkage covariance modelCore shrinkage covariance model, and the tensor factor model. To illustrate the empirical application of tensor-based covariance matrices, Sect. 10.4 presents two real examples including speech recognition and object tracking.

Date: 2026
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-08796-6_10

Ordering information: This item can be ordered from
http://www.springer.com/9783032087966

DOI: 10.1007/978-3-032-08796-6_10

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().