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Ltd
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John Wiley & Sons, Inc.
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© ISTE Ltd 2020
The rights of Mikhail Moklyachuk 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: 2020943973
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-78630-683-8
Notations
| ℕ | Set of natural numbers |
| ℤ | Set of integer numbers |
| ℤ+ | Set of non-negative integer numbers |
| ℝ | Set of real numbers |
 |
Extended set of real numbers |
| ℚ | Set of rational numbers |
| ℝn | Set of real n-vectors |
| ℝm × n | Set of real m × n-matrices |
| ℝ+ | Set of non-negative real numbers |
| ℝ++ | Set of positive real numbers |
| ℂ | Set of complex numbers |
| ℂn | Set of complex n-vectors |
| ℂm × n | Set of complex m × n-matrices |
 |
Set of symmetric n × n-matrices |
 |
Set of symmetric positive semidefinite n × n-matrices |
 |
Set of symmetric positive definite n × n-matrices |
 |
Identity matrix |
| X ⊤ | Transpose of matrix X |
| tr (X) | Trace of matrix X |
| λi(X) | ith largest eigenvalue of symmetric matrix X |
| 〈· , ·〉 | Inner product |
| x ⊥ y | Vectors x and y are orthogonal: 〈x, y〉 = 0 |
| V ⊥ | Orthogonal complement of subspace V |
| diag(X) | Diagonal matrix with diagonal entries x1, … , xn |
| rank (X) | Rank of matrix X |
| ‖·‖ | A norm |
| ‖·‖* | Dual of norm ‖·‖ |
| ‖ x ‖2 | Euclidean norm of vector x |
| x ⪯ y | Componentwise inequality between vectors x and y |
| x ≺ y | Strict componentwise inequality between vectors x and y |
| X ⪯ Y | Matrix inequality between symmetric matrices X and Y |
| X ≺ Y | Strict matrix inequality between symmetric matrices X and Y |
| X ⪯K Y | Generalized inequality induced by proper cone K |
| X ≺K Y | Strict generalized inequality induced by proper cone K |
| int X | Interior of set X |
| ri X | Relative interior of set X |
| conv X | Convex hull of set X |
| aff X | Affine hull of set X |
| cone X | Conic hull of set X |
| Lin X | Linear hull of set X |
 |
Closure of set X |
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