Abstract
No beginner’s course in mathematics can do without linear algebra. According to current international standards it is presented axiomatically. It is a second generation mathematical model with its roots in Euclidean geometry, analytical geometry, and the theory of systems of linear equations. This brings pedagogical difficulties. Beginners with a shaky background in geometry and algebraic computation who also have difficulties with abstractions are really not ripe for the study of linear algebra. On the other hand, there is no need to exaggerate the difficulties. The theory is very simple, has few theorems and is free from complicated proofs. It is also a must. Not being familiar with the concepts of linear algebra such as linearity, vector, linear space, matrix, etc., nowadays amounts almost to being illiterate in the natural sciences and perhaps in the social sciences as well.
Keywords
Banach Space Linear Space Linear Algebra Euclidean Geometry Finite DimensionPreview
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Literature
- Linear algebra is treated in innumerable textbooks, most of them quite adequate. The acknowledged masterpiece is Finite-dimensional Vector Spaces (formerly van Nostrand, now Springer-Verlag), by Paul Halmos. The field of functional analysis has been in a state of constant growth since the 1930s, and the literature is now truly enormous. Its bible is a book by S. Banach from 1932, Théorie des opérations linéaires (Math. Monographs, Warsaw). This work retains its freshness but is now obsolete. It is advisable to start with a simple text like Elements of Functional Analysis, by Maddox (Cambridge University Press), and then go on to an encyclopedic book like Functional Analysis, by Reed and Simon (Methods of Mathematical Physics, vol. 1, Academic Press (1972).Google Scholar