for the Fall semester of 2026-2027.

The Linear Algebra classes of Mathematics I – ADIN001NABB.

Important information

The syllabus can be downloaded, but the summary of the most important part is as follows.

• Attendance is compulsory in the classes.
• The Office Hours is in S 208/b at Monday 19.00. Registration via e-mail is required not later than 7pm of the actual day before.
• Attendance is compulsory in the classes.
• The precise schedule of the quizzes:
  • Week 3 (September 28)
  • Week 6 (October 19)
  • Week 9 (November 16)
  • Week 12 (December 7)

Grading

• Each of the four mini quizzes is worth a maximum of 5 points.
• The final written exam is worth 30 points.
• Altogether, a maximum of 50 points can be earned from the written components of the course.
• The written examination is scheduled for the very first week of the examination period.

All regulations and conditions are governed by the University’s Code of Studies and Examinations.

Weekly Schedule

The week-by-week schedule is as follows:

1. Elements download
   • Vectors
   • Linear Combination
   • Subspaces
   • Linearly independent systems
   • Linearly dependent systems
   • Basic properties of independent systems
   • Gauss-Jordan elimination
2. Basis
   • Basis
   • Basis transformation
   • Applications
3. Matrix download
   • Inner product
   • Concept of Matrices
   • Operations on matrices
   • Multiplication of matrices
   • Powers of matrix
   • Rank theorem
4. Factoring matrices download
   • System of linear equations
   • Factoring matrices
   • Rank–Nullity theorem
   • Problems
5. System of linear equations download
   • Solution of homogeneous linear system of equations
   • Solution of nonhomogeneous linear system of equations
6. The concept of the inverse matrix download
   • Matrix equations
   • Inverse matrix
7. Quadratic forms download
   • Definition of quadratic froms
   • Dyadic decomposition
     • Dyad is the matrix of a complete square
     • High school method for small size
     • Professional method with Gaussian Elimination
   • Problems
   • Definiteness of a quadratic form
   • Summary
8. Determinant download
   • Parity of permutations
   • The concept of determinant
   • Special cases when the size is 1,2, or 3
   • Properties
   • Compute the determinnant using Gauss-Jordan elimination
   • Expension by minors
   • Characteristic polynomial
9. Diagonalize a matrix download
   • Concept of eigenvalue and eigenvector
   • The G-J elimination to find the eigenvalues and the eigenvectors.
   • Diagonalizable matrices.
   • Problems
10. Preparation for the final exam
    • Mock exam