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 PMA 4.102
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 Jan 10: (course details,) row reduction; 1.2 in the notes.
- Thu Jan 12: vector equations, matrix equation Ax=b; 1.3 and 1.4 in the notes.
- Tue Jan 17: solution sets, linear independence; 1.5, and 1.6 in the notes.
- Thu Jan 19: linear transformations, matrix of a linear transformation; 1.8, and 1.9 in the notes.
- Tue Jan 24: some special matrices, matrix operations; 2.0 and 2.1 in the notes.
- Thu Jan 26: matrix operations, inverse of a matrix; 2.1 and 2.2 in the notes.
- Tue Jan 31: classes cancelled.
- Thu Feb 2: classes cancelled.
- Tue Feb 7: inverse of a matrix, definition of the determinant; 2.2 and 3.1 in the notes, .
- Thu Feb 9: midterm exam 1.
- Tue Feb 14: properties of the determinant, vector spaces and subspaces; 3.2 and 4.1 in the notes.
- Thu Feb 16: vector spaces and subspaces; 4.1 in the notes.
- Tue Feb 21: linear transformations; 4.2 in the notes.
- Thu Feb 23: linear transformations, bases; 4.2 and 4.3 in the notes.
- Tue Feb 28: bases, coordinates; 4.3 and 4.4 in the notes.
- Thu Mar 2: bases, coordinates; 4.3 and 4.4 in the notes.
- Tue Mar 7: dimension of a vector space, rank; 4.5 and 4.6 in the notes.
- Thu Mar 9: eigenvalues and eigenvectors; 5.1 in the notes.
- Tue Mar 21: the characteristic equation; 5.2 in the notes.
- Thu Mar 23: midterm exam 2.
- Tue Mar 28: matrix representation and diagonalization; 5.3 in the notes.
- Thu Mar 30: complex eigenvalues, inner products; 5.4 and 6.1 in the notes.
- Tue Apr 4: inner products, orthogonality; 6.1 and 6.2 in the notes.
- Thu Apr 6: orthogonality; 6.2 in the notes.
- Tue Apr 11: orthogonal projections; 6.3 in the notes.
- Thu Apr 13: minimization and least squares; 6.4 in the notes.
- Tue Apr 18: diagonalization; 7.1 in the notes.
- Thu Apr 20: quadratic forms; 7.2 in the notes.