MAT 142 - Linear Algebra II

Course Objectives

1. To teach the concept of inner product, inner product space and diagonalization methods.
2. By reminding the basic subjects of linear transformations to teach the concept of eigenvalues and eigenvectors.
3. To give ability to calculate the eigenvalues, eigenvectors of a matrix, and in terms of similarity transformation to teach the conditions in order to obtain the diagonal.
4. To teach the relation between the eigenvalues and quadratic forms.
5. To teach Analytic Geometry applications of Linear Algebra concepts.

Course Description

Inner Product Spaces; Standard inner product, Orthogonal subspaces, Orthogonal complement of a subspace, Inner product spaces, Cauchy-Schwarz inequality, Normed space, Orthogonal basis, Orthogonal matrices, Gram-Schmidt orthogonalization methods.
Linear Transformations and Matrices; Definition of a linear transformations, The kernel and range of a linear transformation, Matrix representations of a linear transformations, Similarity.
Eigenvalues and Eigenvectors; Definition, Cayley-Hamilton Theorem, Diagonalization and Similar matrices, Diagonalization of symmetric matrices.
Applications of Eigenvalues and Eigenvectors; Quadratic forms, Conic sections, Quadric surfaces.