Algebraic and Computational Aspects of Real Tensor Ranks

• Main Authors: Sakata, Toshio (Author), Sumi, Toshio (Author), Miyazaki, Mitsuhiro (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Tokyo : Springer Japan : Imprint: Springer, 2016.
• Edition: 1st ed. 2016.
• Series: SpringerBriefs in Statistics,
• Subjects: Statistics.; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.; Statistics and Computing/Statistics Programs.; Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law.

This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real...

Table of Contents:

• Basics of Tensor Rank
• 3-Tensors
• Simple Evaluation Methods of Tensor Rank
• Absolutely Nonsingular Tensors and Determinantal Polynomials
• Maximal Ranks
• Typical Ranks
• Global Theory of Tensor Ranks
• 2 × 2 × · · · × 2 Tensors.