Linear Algebra Ii

This is the second of two courses on linear algebra. This course is compulsory for students of mathematical sciences, and it is a prescribed elective course for students from other schools as well. The course aims to present a careful treatment of the principal topics of linear algebra, such as general vector spaces, linear transformations, diagonalization, and inner product spaces, and to illustrate the power of the subject through a variety of applications. After learning this course, you will be able to make connections between the abstract settings and the concrete problems studied in Linear Algebra I. The main topics are: 1. General vector spaces: Real/Complex Vector Space, Subspaces, Linear Combination & Span, Linear Independence, Basis, Coordinate Vectors, Finite Dimensional Space and its Dimension, Basis Construction. 2. Linear transformations: Linear Transformation & Examples, Rank-Nullity Theorem, Representation by Matrices, Change of basis & Applications. 3. Eigenvectors & eigenvalues: Eigen values/vectors of Matrices and Linear Transformations, Characteristic Polynomials, Eigen space, Diagonalization & Applications. 4. Inner product spaces: Inner Product, Orthogonality, Orthonormal sets, Gram-Schmidt process.