The objective of this course unit is to introduce the essential mathematical methods used in AI, enabling students to understand how mathematics supports the foundational techniques of AI. Students who complete this course unit should be able to:

1. Apply concepts of vectors and matrices in AI
2. Decompose matrix multiplication
3. Execute LU and QR decompositions and calculate the Moore-Penrose pseudoinverse
4. Diagonalize matrices and understand their implications in AI
5. Analyze the properties of symmetric and positive semidefinite matrices
6. Perform Cholesky factorization and apply it in optimization
7. Utilize variable separation in optimization
8. Use convex objective functions and apply the gradient descent method in AI
9. Identify and address the specifics of optimization in AI
10. Calculate derivatives with respect to vectors in optimization problems
11. Execute SVD from an algebraic and optimization perspective
12. Identify its applications in AI