Linear Algebra II

This is a second course on Linear Algebra at USP. The first course, namely MA111 (Calculus I and Linear Algebra I), covered the first 3 chapters of the textbook by Larson, Edwards and Falvo. This course covers the rest of the chapters of the textbook. Students having difficulty understanding the various topics in this course should go back and read relevant sections from chapters 1 to 3 of the textbook. The primary goal of this course is to look at vector spaces, inner product spaces, linear transformations, eigenvalues and eigenvectors and their applications. The topics that we will cover in this course are as follows: Vectors in Rn, Vector spaces, Subspaces of vectors spaces, Spanning sets and linear independence, Basis and dimension, Rank of a matrix and systems of linear equations, Coordinates and change of basis, Applications of vectors spaces, Length and dot product in Rn, Inner product spaces, Orthonormal basis: Gram-Schmidt process, Mathematical models and least squares analysis, Applications of inner product spaces, Introduction to linear transformations, Kernel and range of linear transformations, Matrices of linear transformations, Transition matrices and similarity, Applications of linear transformations, Eigenvalues and eigenvectors, Diagonalization, Symmetric matrices and orthogonal diagonalization, Application of eigenvalues and eigenvectors.