Includes indexes.

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.

In the spirit of the author's Basic Language of Mathematics, this companion volume is a careful exposition of the concepts and processes of Linear Algebra. It stresses cautious and clear explanations, avoiding reliance on co–ordinates as much as possible, and with special, but not exclusive, attention to the finite–dimensional situation. It is intended to also serve as a conceptual and technical background for use in geometry and analysis as well as other applications.

Electronic reproduction. Singapore : World Scientific Publishing Co., 2015. System requirements: Adobe Acrobat Reader. Mode of access: World Wide Web. Available to subscribing institutions.