Math 115A: Linear Algebra

Linear Algebra is the study of vector spaces and linear maps between vector spaces. In Math 33A, students learned how to manipulate vectors and matrices to understand how to solve systems of linear equations and specifically studied linear algebra in the context of euclidean space. This course aims to give a more abstract view of the topic preparing students for proof based course. The material covered in Math 115A includes linear independence, bases, orthogonality, the Gram-Schmidt process, linear transformations, eigenvalues and eigenvectors, and diagonalization of matrices. These topics are all covered in Math 33A though only in the context of Euclidean space. Topics in Math 115A that go beyond Math 33A include inner product spaces, adjoint transformations, and the spectral decomposition theorem for self-adjoint operators.