Introduction to Vectors and Tensors Vol 2 (Bowen 246). - Index of

viii CONTENTS OF VOLUME 2
Section 17. Special Types of Linear Transformations…………………… 97
Section 18. The Adjoint of a Linear Transformation…………………….. 105
Section 19. Component Formulas………………………………………... 118
CHAPTER 5. Determinants and Matrices…………………………………………… 125
Section 20. The Generalized Kronecker Deltas
and the Summation Convention……………………………… 125
Section 21. Determinants…………………………………………………. 130
Section 22. The Matrix of a Linear Transformation……………………… 136
Section 23 Solution of Systems of Linear Equations…………………….. 142
CHAPTER 6 Spectral Decompositions……………………………………………... 145
Section 24. Direct Sum of Endomorphisms……………………………… 145
Section 25. Eigenvectors and Eigenvalues……………………………….. 148
Section 26. The Characteristic Polynomial………………………………. 151
Section 27. Spectral Decomposition for Hermitian Endomorphisms…….. 158
Section 28. Illustrative Examples…………………………………………. 171
Section 29. The Minimal Polynomial……………………………..……… 176
Section 30. Spectral Decomposition for Arbitrary Endomorphisms….….. 182
CHAPTER 7. Tensor Algebra………………………………………………………. 203
Section 31. Linear Functions, the Dual Space…………………………… 203
Section 32. The Second Dual Space, Canonical Isomorphisms…………. 213
Section 33. Multilinear Functions, Tensors…………………………..….. 218
Section 34. Contractions…......................................................................... 229
Section 35. Tensors on Inner Product Spaces……………………………. 235
CHAPTER 8. Exterior Algebra……………………………………………………... 247
Section 36. Skew-Symmetric Tensors and Symmetric Tensors………….. 247
Section 37. The Skew-Symmetric Operator……………………………… 250
Section 38. The Wedge Product………………………………………….. 256
Section 39. Product Bases and Strict Components……………………….. 263
Section 40. Determinants and Orientations………………………………. 271
Section 41. Duality……………………………………………………….. 280
Section 42. Transformation to Contravariant Representation……………. 287
INDEX…………………………………………………………………………………….x