Course Syllabus MA 401

Course Syllabus
MA 401 Linear Algebra

Lectures will be in 216 at 2 PM on Mondays, Wednesdays and Thursdays.

Course Text

Linear Algebra by Friedberg, Insel and Spence,
Linear Algebra by Hoffman and Kunze

Course Content

Vector spaces over fields, subspaces, bases and dimension.
Systems of linear equations, matrices, rank, Gaussian elimination.
Linear transformations, representation of linear transformations by matrices, rank-nullity theorem, duality and transpose.
Determinants, Laplace expansions, cofactors, adjoint, Cramer's Rule.
Eigenvalues and eigenvectors, characteristic polynomials, minimal polynomials, Cayley-Hamilton Theorem, triangulation, diagonalization, rational canonical form, Jordan canonical form.
Inner product spaces, Gram-Schmidt ortho-normalization, orthogonal projections, linear functionals and adjoints, Hermitian, self-adjoint, unitary and normal operators.
Spectral Theorem for normal operators. Bilinear forms, symmetric and skew-symmetric bilinear forms, real quadratic forms.

Grading

Quizzes, Homework	: 35%
Midsem	: 25%
Final	: 40%

Homeworks

Homeworks will be assigned reguarly .
Homeworks are meant to help you learn the material regularly and unless you do them by yourself, you will not be able to do well on the tests.

Exams

Quiz weeks have been specified in the class calendar. No make up quizzes will be offered.
Make up exams will be offered only when you have a valid excuse.