MAT 142E - Linear Algebra II

Course Objectives

1- To teach the concept of inner product, iner product space and diagonalization methods,
2- By reminding the basic subjects of linear transformations to teach the concept of eigen
values and eigen vectors.
3- To give ability to calculate the eigenvalues, eigenvactors 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, inner product spaces, normed space, Cauchy-Schwarz
inequality, orthogonal basis, orthogonal matrices, Gram-Schmidt orthogonalization methods.
Linear transformations; Definition of Linear transformation, Matrix Representations of
Linear Transformations, Similarity.
Eigenvalues and Eigenvectors; diagonalization, Cayley-Hamilton Theorem, quadratic forms,
Conic sections, Quadratic surfaces