Instructor: Anatolii Grinshpan

Office hours: Mon 2-3 & Wed 1-3, Korman 249.

Course information Academic
calendar Tutoring center

Mar 31. Introduction to the course. Gauss-Jordan
elimination.

Apr
2. Reduced
echelon form. Leading and free variables. Rank. Example.

Reading:
1.1, 1.2. Problems

Apr 7. Quiz
1 (Gaussian elimination). Tall, long, square.
The structure of solutions. Vectors.

Apr 9. Linear combinations of vectors. Matrix-vector
product and its properties.

Reading:
1.3. Problems

Apr 14.
Quiz 2 (matrix-vector product). Linear transformations.
The matrix of a transformation.

Apr 16. Projections, reflections, rotations and their matrices. Inversion. Matrix product.

Reading:
2.1, 2.2. Problems Problems

Apr 21. Properties of matrix
multiplication. Reading: 2.3. Problems

Apr 23. Midterm 1 (lectures of March 31 - April 21).

Apr 28. Invertible transformations. Matrix
inversion. Inverses of elementary matrices.
Reading: 2.4. Problems

Apr 30.
Quiz 3 (matrix inversion). Transpose. Block
multiplication and inversion. Image of a linear
transformation. Span.

May 5. Kernel of a linear transformation. Subspaces.
Linear independence. Reading: 3.1, 3.2. Problems
Problems

May 7.
Quiz 4 (image and kernel). Vector relations. Basis and dimension. Basis for the kernel. Basis for the image. Rank-nullity theorem.

Subspaces associated to
a matrix. Reading: 3.3. Problems

May 12. Characterizations of linear independence. Characterizations
of invertibility. Coordinates
relative to a given basis.

May 14.
Quiz 5 (basis and dimension). The matrix of a linear
transformation relative to a given basis.

Reading:
3.4. Problems

May 19. Orthogonal projections and orthonormal bases. Reading: 5.1. Problems

May 21. Midterm 2 (lectures of April 28 - May 19).

May 26. Matrix of the orthogonal projection. Orthogonal
transformations and matrices. Determinants.
Reading: 5.3. Problems

May 28. Properties of the determinant. Reading: 6.1, 6.2. Problems (answers). Eigenvalues and eigenvectors.

June 2. Quiz 6 (determinants). Eigenspaces and eigenbases.
Examples. Reading: 7.1-7.3. Problems

June
4. Cross-product
transformation. Diagonalization. Symmetric matrices.

Practice
quizzes: Set
1 Set
2 Set
3 Set 4 Set 5 Set
6.

*June 11. Questions session:
10-Noon, Stratton 101*.
Example.

June 12. Final exam: 10:30-12:30 AM, Lebow 241.