Course info

Systems of Linear Equations, Matrices and Elementary Row Operations, Row-Reduced Echelon Matrices . Vector Spaces, Subspaces, Bases and Dimension, Ordered basis and coordinates. Linear transformations, Rank-Nullity Theorem, The algebra of linear transformations, Isomorphism, Matrix representation of linear transformations, Linear Functionals, Annihilator, Double dual, Transpose of a linear transformation . Characteristic Values and Characteristic Vectors of linear transformations, Diagonalizability, Minimal polynomial of a linear transformation, Cayley-Hamilton Theorem, Invariant Subspaces, Direct-sum decompositions, Invariant Direct sums, The primary decomposition theorem, Cyclic subspaces and annihilators, Cyclic decomposition, rational, Jordan forms. Inner Product Spaces, Orthonormal Basis, Gram-Schmidt Theorem.