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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#sympy #python

24.45 GEEK