SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python.

SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python. SymPy is used in many projects such as Cadabra, ChemPy, EinsteinPy, galgebra, Lcapy, SageMath, SfePy, Spyder, yt, etc. SimPy is free, lightweight and Python-based. In this lecture, we focus on SymPy's Linear Algebra features. We outline the contents of this lecture as follows:

00:00 Introduction 00:37 Setting Jupyter 01:16 Matrix Creation 02:29 Matrix-Vector Product 02:40 Matrix Addition 03:15 Matrix-Matrix Product 03:40 Matrix Scaling 03:49 Power of Matrices 04:24 Matrix Inversion 04:52 Matrix Determinant 05:50 Matrix Transposition 06:02 Accessing Rows and Columns 07:04 Deleting Rows and Columns 08:15 Inserting Rows and Columns 10:16 Identity Matrix 11:00 Zeros Matrix 11:24 Ones Matrix 11:43 Matrix Dimensions 12:02 Diagonal Matrix 12:47 Block Diagonal Matrix 14:55 Reduced Row Echelon Form (rref) 19:27 Null Space 21:09 Column Space 24:27 Eigenvalues & Algebraic Multiplicity 26:35 Eigenvectors 29:27 Diagonlization: Eigen Value Decomposition 31:10 Characteristic Polynomial 32:50 LU Decomposition 34:15 Check if Echelon 34:53 Summary 36:52 Outro

Instructor: Dr. Ahmad Bazzi

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