xii
CONTENTS
A.2 Important Structures
A.2.1 Groups
A.2.2 Linear spaces: V n,
A n
A.2.3 Metric spaces
A.2.4 Normed spaces, Euclidean norms
A.3 Our Framework for Electromagnetism: E 3
A.3.1 Grad, rot, and div
A.3.2 Digression: the so-called "axial vectors"
A.3.3 The Poincar6 lemma
A.3.4 Symmetry in E 3
A.4 Glimpses of Functional Analysis
A.4.1 Completion, principle of extension by continuity
A.4.2 Integration
A.4.3 Hilbert spaces
A.4.4 Closed linear relations, adjoints
References
282
282
283
288
291
294
294
296
298
300
304
304
306
310
315
317
APPENDIX B LDL t Factorization and Constrained
Linear Systems
B.1 Nonnegative Definite Matrices
B.2 A Digression about Programming
B.3 The LDL t Factorization
B.4 Application to Constrained Linear Systems
References
319
319
322
324
326
328
APPENDIX C A Cheaper Way to Complementarity
C.1 Local Corrections
C.2 Solving Problem (14)
C.3 Conclusion and Speculations
329
330
333
336
Author Index
339
Subject Index
343
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