for the Fall semester of 2024-2025.

The Linear Algebra classes of Mathematics I – ADIN001NABB. The Course Syllabus contains more detailed information, the most important part is as follows:

Important information

• The Office Hours is in S 208/b at Monday 17.20. Registration via e-mail is required not later than 7pm of the actual day before.
• Attendance is compulsory in the classes.
• The exact date of the Mini Quizzes are as follows:

    Week 3,
    Week 6, 
    Week 9,
    Week 12.
  

  No reschedule or makeup of the mini quizzes.

• The Final Exam is scheduled to the first week of the examination period.

Grading

• You will receive 5-5 points at maximum for your 4 Mini quizzes, but the best 3 is form 15 points. 25 points for the Final exam. Thus 40 points can be collected during the written part of examination.
• You have optional oral exams at the examination periode for 10 points. All rules and conditions are regulated by the University Code of Study and Exams.

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The week by week schedule is as follows. Handouts compiled by the instructor are available here, after each classes.

1. Elements of Linear Algebra
   • Vectors
   • Linear Combination
   • Basis
   • Basis transformation
   • Applications
2. Matrix
   • Inner product
   • Concept of Matrices
   • Operations on matrices
   • Multiplication of matrices
   • Powers of matrix
   • Rank theorem
3. Factoring matrices
   • System of linear equations
   • Factoring matrices
   • Problems
4. System of linear equations
   • Solution of homogeneous linear system of equations
   • Solution of nonhomogeneous linear system of equations
5. The concept of the inverse matrix
   • Matrix equations
   • Inverse matrix
6. Quadratic forms
   • 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
7. Determinant
   • 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
8. Diagonalize a matrix
   • Concept of eigenvalue and eigenvector
   • The G-J elimination to find the eigenvalues and the eigenvectors.
   • Diagonalizable matrices.
   • Problems
9. Preparation for the final exam
   • Mock exam