Linear Algebra

Ch. 1. Linear spaces and linear mappings. 11. Linear spaces. 12. Linear mappings. 13. Subspaces. 14. Linear partitions. 15. Supplements -- ch. 2. Properties of linear mappings. 21. Linear invertibility. 22. Cancellability and factorization -- ch. 3. Linear products and coproducts. 31. Linear products. 32. Linear coproducts. 33. Decompositions -- ch. 4. Families in linear spaces. 41. Linear combination. 42. Linear independence. 43. Linear independence, spanning, bases -- ch. 5. Finite dimension. 51. Matrices. 52. Finite-dimensional spaces. 53. Finite dimension and linear mappings. 54. Finite- and infinite-dimensional spaces -- ch. 6. Duality. 61. Dual spaces and transposes. 62. Annihilators. 63. Higher-order dual spaces and transposes. 64. Biorthogonal families -- ch. 7. Duality and finite dimesion. 71. Duality for finite-dimensional spaces. 72. Dual bases and matrices. 73. The trace form. 74. The canonical identifications