Math 2568: Linear Algebra. (Instructor: Sergei Chmutov)

Spring 2024. Tentative Daily Schedule

1/08 (Mon)
Introduction. Systems of linear equations. (Sec.1.1) 1/10 (Wed)
Elementary row operations. (Sec.1.1) 1/12 (Fri)
Echelon Form and Gaussian-Jordan Elimination.(Sec.1.2).

1/15 (Mon)
NO CLASSES. Martin Luther King Day. 1/17 (Wed)
Consistent Systems of linear Equations. (Sec.1.3). 1/19 (Fri)
Matrix Operations.
(Sec.1.5).

1/22 (Mon)
Algebraic Properties of Matrix operations. (Sec.1.6). 1/24 (Wed)
Linear Independence and Nonsingular Matrices. (Sec.1.7). 1/26 (Fri)
Matrix Inverses and Their Properties. (Sec.1.9)

1/29(Mon)
Vectors in Plane and in Space. (Sec.2.1,2.2) 1/31 (Wed)
Review for midterm 1. 2/02 (Fri)
Midterm #1.

2/05 (Mon)
The Dot Product. (Sec.2.3) 2/07 (Wed)
The Cross Product. (Sec.2.3) 2/09 (Fri)
Introduction to Vector Spaces. (Sec.3.1)

2/12 (Mon)
Vector Space Properties of Rⁿ. (Sec.3.2) 2/14 (Wed)
Examples of Subspaces. (Sec.3.3) 2/16 (Fri)
Bases for Subspaces.
(Sec.3.4)

2/19 (Mon)
Dimension. (Sec.3.5) 2/21 (Wed)
Vector Spaces. (Sec.5.2). 2/23 (Fri)
Subspaces. (Sec.5.3)

2/26 (Mon)
Linear Independence and Bases. (Sec.5.4) 2/28 (Wed)
Coordinates. (Sec.5.4) 3/01 (Fri)
Orthogonal Bases for Subspaces. (Sec.3.6)

3/04 (Mon)
Inner-Product Spaces, Orthogonal Bases.
(Sec.5.6) 3/06 (Wed)
Review for midterm 2. 3/08 (Fri)
Midterm #2.

3/11 (Mo) --- 3/15 (Fri)
NO CLASSES. Spring Break.

3/18 (Mon)
Linear Transformations from Rⁿ to R^m. (Sec.3.7) 3/20 (Wed)
Linear Transformations. (Sec.5.7) 3/22 (Fri)
Operations with Linear Transformations. (Sec.5.8)

3/25 (Mon)
Matrix Representations for Linear Transformations. (Sec.5.9) 3/27 (Wed)
Introduction to Determinants. (Sec.6.1, 4.2) 3/29 (Fri)
Cofactor Expansions of Determinants. (Sec.6.2)

4/01 (Mon)
Elementary operations and Determinants. (Sec.4.3) 4/03 (Wed)
Elementary operations and Determinants. (Sec.6.3) 4/05 (Fri)
Cramer's Rule. (Sec.6.4)

4/08 (Mon)
The Eigenvalue Problem for 2x2 Matrices. (Sec.4.1) 4/10 (Wed)
Eigenvalues and Characteristic Polynomial. (Sec.4.4) 4/12 (Fri)
Eigenvalues and Characteristic Polynomial. (Sec.4.4)

4/15 (Mon)
Eigenvectors and Eigenspaces. (Sec.4.5) 4/17 (Wed)
Complex Eigenvalues and Eigenvectors. (Sec.4.6) 4/19 (Fri)
Similarity Transformations and Diagonalization. (Sec.4.7)

4/22 (Mon)
Review for the final.

4/30 (TUE)
FINAL, 12:00 - 1:45 PM

1/08 (Mon) Introduction. Systems of linear equations. (Sec.1.1)	1/10 (Wed) Elementary row operations. (Sec.1.1)	1/12 (Fri) Echelon Form and Gaussian-Jordan Elimination.(Sec.1.2).
1/15 (Mon) NO CLASSES. Martin Luther King Day.	1/17 (Wed) Consistent Systems of linear Equations. (Sec.1.3).	1/19 (Fri) Matrix Operations. (Sec.1.5).
1/22 (Mon) Algebraic Properties of Matrix operations. (Sec.1.6).	1/24 (Wed) Linear Independence and Nonsingular Matrices. (Sec.1.7).	1/26 (Fri) Matrix Inverses and Their Properties. (Sec.1.9)
1/29(Mon) Vectors in Plane and in Space. (Sec.2.1,2.2)	1/31 (Wed) Review for midterm 1.	2/02 (Fri) Midterm #1.
2/05 (Mon) The Dot Product. (Sec.2.3)	2/07 (Wed) The Cross Product. (Sec.2.3)	2/09 (Fri) Introduction to Vector Spaces. (Sec.3.1)
2/12 (Mon) Vector Space Properties of Rⁿ. (Sec.3.2)	2/14 (Wed) Examples of Subspaces. (Sec.3.3)	2/16 (Fri) Bases for Subspaces. (Sec.3.4)
2/19 (Mon) Dimension. (Sec.3.5)	2/21 (Wed) Vector Spaces. (Sec.5.2).	2/23 (Fri) Subspaces. (Sec.5.3)
2/26 (Mon) Linear Independence and Bases. (Sec.5.4)	2/28 (Wed) Coordinates. (Sec.5.4)	3/01 (Fri) Orthogonal Bases for Subspaces. (Sec.3.6)
3/04 (Mon) Inner-Product Spaces, Orthogonal Bases. (Sec.5.6)	3/06 (Wed) Review for midterm 2.	3/08 (Fri) Midterm #2.

3/18 (Mon) Linear Transformations from Rⁿ to R^m. (Sec.3.7)	3/20 (Wed) Linear Transformations. (Sec.5.7)	3/22 (Fri) Operations with Linear Transformations. (Sec.5.8)
3/25 (Mon) Matrix Representations for Linear Transformations. (Sec.5.9)	3/27 (Wed) Introduction to Determinants. (Sec.6.1, 4.2)	3/29 (Fri) Cofactor Expansions of Determinants. (Sec.6.2)
4/01 (Mon) Elementary operations and Determinants. (Sec.4.3)	4/03 (Wed) Elementary operations and Determinants. (Sec.6.3)	4/05 (Fri) Cramer's Rule. (Sec.6.4)
4/08 (Mon) The Eigenvalue Problem for 2x2 Matrices. (Sec.4.1)	4/10 (Wed) Eigenvalues and Characteristic Polynomial. (Sec.4.4)	4/12 (Fri) Eigenvalues and Characteristic Polynomial. (Sec.4.4)
4/15 (Mon) Eigenvectors and Eigenspaces. (Sec.4.5)	4/17 (Wed) Complex Eigenvalues and Eigenvectors. (Sec.4.6)	4/19 (Fri) Similarity Transformations and Diagonalization. (Sec.4.7)
4/22 (Mon) Review for the final.