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Tensor and Covariance Matrices

In: Covariance Analysis and Beyond

Author

Listed:
  • 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)

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.

Suggested Citation

  • Wei Lan & Chih-Ling Tsai, 2026. "Tensor and Covariance Matrices," Springer Books, in: Covariance Analysis and Beyond, chapter 0, pages 183-202, Springer.
    • Handle: RePEc:spr:sprchp:978-3-032-08796-6_10
    DOI: 10.1007/978-3-032-08796-6_10
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