![]() |
Math 115AB: Linear Algebra |
|
Catalog Description
115A. Linear Algebra. (5) Lecture, three hours;
discussion, two hours. Requisite: course 33A. Techniques of proof, abstract
vector spaces, linear transformations, and matrices; determinants; inner product
spaces; eigenvector theory. P/NP or letter grading.
115B. Linear Algebra. (4) Lecture, three hours; discussion, one hour. Requisite: course 115A. Linear transformations, conjugate spaces, duality; theory of a single linear transformation, Jordan normal form; bilinear forms, quadratic forms; Euclidean and unitary spaces, symmetric skew and orthogonal linear transformations, polar decomposition. P/NP or letter grading. |
Additional Information
Math 115A is a core mathematics course required of all the various mathematics
majors. The course material can be regarded as an elaboration of the linear
algebra already covered in Math 33A. However, the level of abstraction and the
emphasis on proof technique make this a difficult course for many students.
Successful students emerge from the experience not only with a better understanding
of linear algebra, but also with a higher level of mathematical maturity, better
equipped to deal with abstract concepts.
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. Three or four sections of Math 115A are offered each term. Also, an honors
version Math 115AH runs parallel to Math 115A in some quarters. The content of Math 115AH is as follows: |