Fundamentals from Linear Algebra Ghan S. Bhatt and Ali Sekmen Mathematical Sciences and Computer Science College of Engineering Tennessee State University.

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Presentation transcript:

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