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Vector Space : Definition and Examples of Vector Spaces, Subspaces, Algebra of subspaces, Linear span, Linear dependence and independence of vectors, Basis and Dimension of a vector space, Basis and dimension of subspace, Direct sums and complements. Linear Transformations, Rank and Nullity of a linear transformation, Vector space of linear transformations. Linear transformation and matrices, Change of basis. Characteristic roots and characteristic vectors, Algebraic and Geometric multiplicity of a characteristic value, Cayley?Hamilton theorem, Diagonalizable operators and matrices. Minimal polynomial of a linear operator (matrix).

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