1. Fundamentals from Linear Algebra Ghan S. Bhatt and Ali Sekmen Mathematical Sciences and Computer Science College of Engineering Tennessee State University 1 st Annual Workshop on Data Sciences

2. Part I Some Linear Algebra Spectral Analysis Singular Value Decomposition Presenter Dr. Ghan S. Bhatt

3. Definitions

4. Range and Null Spaces

6. Definitions

7. Eigenvalues - Eigenvectors

11. Symmetric Matrices

13. Projection on a Vector

14. Projection on a Subspace

15. Singular Value Decomposition

19. Important Lemma

20. Recall – Linear Mapping

22. General Matrix Norms

23. An Intuitive Matrix Norm Although it is useful, it is not suitable for large set of problems and we need another definition of matrix norms This satisfies the general matrix norm properties

24. Induced Matrix Norms

25. Matrix p-Norm

26. More on Matrix Norms