Note:
Access to document files (lecture notes, exams, homework)
is restricted to
hosts from
.utexas.edu
or to user class with the appropriate password
(posted on Canvas).
LECTURES: Tue Thu 12:30 pm - 2:00 pm, in GSB 2.126
Attending classes is mandatory.
Lecture notes will be posted below one week in advance,
together with a list of topics for the upcoming two lectures.
The class lectures follow the lecture notes,
on a somewhat more basic level than the notes,
including summaries, previews, extra context, etc.
Students are encouraged to ask questions, including homework-related questions.
Lecture notes
Remarks:
The notes are cumulative.
The latest set should be considered work in progress,
so the numbers assigned to theorems, equations, and examples may change.
The indicated date is something like a "target date",
by which the version is meant to be stable.
The sections and subsections in the notes
correspond roughly to those in the textbook.
But the theorems, equations, examples,
and their numbers differ from the textbook.
Syllabus
- Tue Aug 22: (course details,) row reduction; 1.2 in the notes.
- Thu Aug 24: vector equations, matrix equation Ax=b; 1.3 and 1.4 in the notes.
- Tue Aug 29: solution sets, linear independence; 1.5 and 1.7 in the notes.
- Thu Aug 31: linear transformations, matrix of a linear transformation; 1.8, and 1.9 in the notes.
- Tue Sep 5: some special matrices, matrix operations; 2.0 and 2.1 in the notes
- Thu Sep 7: matrix operations, inverse of a matrix; 2.1 and 2.2 in the notes.
- Tue Sep 12: inverse of a matrix, definition of the determinant; 2.2 and 3.1 in the notes.
- Thu Sep 14: properties of the determinant, vector spaces and subspaces; 3.2 and 4.1 in the notes.
- Tue Sep 19: vector spaces and subspaces, linear transformations; 4.1 and 4.2 in the notes.
- Thu Sep 21: midterm exam 1.
- Tue Sep 26: linear transformations, bases; 4.2 and 4.3 in the notes.
- Thu Sep 28: bases, coordinates; 4.3 and 4.4 in the notes.
- Tue Oct 3: bases, coordinates; 4.3 and 4.4 in the notes.
- Thu Oct 5: dimension of a vector space, rank; 4.5 and 4.6 in the notes.
- Tue Oct 10: rank, eigenvalues and eigenvectors; 4.6 and 5.1 in the notes.
- Thu Oct 12: eigenvalues and eigenvectors; 5.1 in the notes.
- Tue Oct 17: the characteristic equation; 5.2 in the notes.
- Thu Oct 19: matrix representation and diagonalization; 5.3 in the notes.
- Tue Oct 24: complex eigenvalues; 5.4 in the notes.
- Thu Oct 26: midterm exam 2.
- Tue Oct 31: inner products; 6.1 in the notes.
- Thu Nov 2: orthogonality; 6.2 in the notes.
- Tue Nov 7: orthogonality, orthogonal projections; 6.2 and 6.3 in the notes.
- Thu Nov 9: orthogonal projections; 6.3 in the notes.
- Tue Nov 14: minimization and least squares; 6.4 in the notes.
- Thu Nov 16: diagonalization; 7.1 in the notes.
- Tue Nov 18: quadratic forms; 7.2 in the notes
- Thu Nov 30: complex inner product spaces; 8 in the notes.