Transcription of Notes on Linear Algebra - Queen Mary University of London
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Notes on Linear Algebra - Queen Mary University of London
Notes on Linear AlgebraPeter J. CameroniiPrefaceLinear Algebra has two aspects. Abstractly, it is the study of vector spaces overfields, and their Linear maps and bilinear forms. Concretely, it is matrix theory:matrices occur in all parts of mathematics and its applications, and everyone work-ing in the mathematical sciences and related areas needs to be able to diagonalisea real symmetric matrix. So in a course of this kind, it is necessary to touch onboth the abstract and the concrete aspects, though applications are not treated the theoretical side, we deal with vector spaces, Linear maps, and bilin-ear forms. Vector spaces over a fieldKare particularly attractive algebraic ob-jects, since each vector space is completely determined by a single number, itsdimension (unlike groups, for example, whose structure is much more compli-cated). Linear maps are the structure-preserving maps or homomorphisms of vec-tor the practical side, the subject is really about one thing: matrices.
Linear algebra has two aspects. Abstractly, it is the study of vector spaces over fields, and their linear maps and bilinear forms. Concretely, it is matrix theory: matrices occur in all parts of mathematics and its applications, and everyone work-ing in the mathematical sciences and related areas needs to be able to diagonalise
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