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
Part I Some Linear Algebra Spectral Analysis Singular Value Decomposition Presenter Dr. Ghan S. Bhatt
Definitions
Range and Null Spaces
Definitions
Eigenvalues - Eigenvectors
Symmetric Matrices
Projection on a Vector
Projection on a Subspace
Singular Value Decomposition
Important Lemma
Recall – Linear Mapping
General Matrix Norms
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
Induced Matrix Norms
Matrix p-Norm
More on Matrix Norms