Gérard Favier - Matrix and Tensor Decompositions in Signal Processing

Table 3.5. Notation for tensors Table 3.6. Matricization by index blocks for different sets of tensors Table 3.7. Block-wise transposition Table 3.8. Hermitian/symmetric tensors by blocks of order P Table 3.9. Block symmetrized tensor χ of a third-order tensor Table 3.10. Outer products of matrices and tensors Table 3.11. Scalar elements of outer products Table 3.12. Matricized and vectorized forms of a rank-one third-order tensor Table 3.13. Mode- p products of a third-order tensor with a matrix Table 3.14. Matrix products and mode- p product Table 3.15. Different types of multiplication with tensors Table 3.16. Orthogonality and idempotence properties Table 3.17. Inverses of orthogonal/unitary tensors Table 3.18. Generalized inverses Table 3.19. Operations with the Einstein product Table 3.20. Properties of the Moore-Penrose pseudo-inverse Table 3.21. LS solutions of tensor linear systems Table 3.22. Matrix operations Table 3.23. Tensor operations

5 Chapter 4Table 4.1. Eigenpairs and generalized eigenpairs for tensors Table 4.2. Properties of hypercubic symmetric tensors

6 Chapter 5Table 5.1. Third-order Tucker model Table 5.2. Tucker-(2,3) and Tucker-(1,3) models Table 5.3. Third-order PARAFAC model Table 5.4. Fourth-order PARAFAC model Table 5.5. Variants of the third-order PARAFAC model Table 5.6. k -rank of certain matrices and essential uniqueness of a third-order ...

7 Appendix Random Variables and Stochastic ProcessesTable A1.1. Some definitions for jointly distributed r.v.s x and y Table A1.2. Definitions of uncorrelated and orthogonal r.v.s x and y Table A1.3. Properties of r.v.s Table A1.4. Definitions and properties of the second-order statistics of real ra...Table A1.5. Definitions and properties for real random signals x ( k ) and y ( k )Table A1.6. Definitions and properties of second-order statistics for stationary...Table A1.7. Second-order statistics of the output of a linear system Table A1.8. Factors of the polyspectra Table A1.9. Bispectra and trispectra of the output of a linear system

1 Cover

2 Table of Contents

3 Title Page Matrices and Tensors with Signal Processing Set coordinated by Gérard Favier Volume 2

4 Copyright First published 2021 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 27-37 St George’s Road London SW19 4EU UK www.iste.co.uk John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA www.wiley.com © ISTE Ltd 2021 The rights of Gérard Favier to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2021938218 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78630-155-0

5 Introduction

6 Begin Reading

7 Appendix Random Variables and Stochastic Processes

8 References

9 Index

10 Other titles from iSTE in Digital Signal and Image Processing

11 End User License Agreement

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