M205 - Linear Algebra

System of Linear Equations, Matrices and elementary row operations, Rowreduced echelon form of matrices, Vector spaces, subspaces, quotient spaces, bases and dimension, direct sums, Linear transformations and their matrix representations, Dual vector spaces, transpose of a linear transformation, Polynomial rings (over a field), Determinants and their properties, Eigenvalues and eigenvectors, Characteristic polynomial and minimal polynomial, Triangulation and Diagonalization, Simultaneous Triangulation and diagonalization, Direct-sum decompositions, Primary decomposition theorem.