SymPy (Symbolic Expressions on Python) | The Linear Algebra Edition | Python # 16

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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

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