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Fundamentals from Linear
Algebra
Ghan S. Bhatt and Ali Sekmen
Mathematical Sciences and Computer Science
College of Engineering
Tennessee State University
1st 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
Range and Null Spaces
Definitions
Eigenvalues - Eigenvectors
Eigenvalues - Eigenvectors
Eigenvalues - Eigenvectors
Eigenvalues - Eigenvectors
Symmetric Matrices
Symmetric Matrices
Projection on a Vector
Projection on a Subspace
Singular Value Decomposition
Singular Value Decomposition
Singular Value Decomposition
Singular Value Decomposition
Important Lemma
Recall – Linear Mapping
Recall – Linear Mapping
General Matrix Norms
An Intuitive Matrix Norm
This satisfies the general matrix norm properties
Although it is useful, it is not suitable for large set of
problems and we need another definition of matrix
norms
Induced Matrix Norms
Matrix p-Norm
More on Matrix Norms