Linear Algebra Using Python Course

The Linear Algebra Course is good for students who want to learn linear algebra. The course discusses various topics of linear algebra. It also uses Python to solve various problems on this subject. The course is also good for students and professionals who want to learn this subject for the purpose of learning cryptanalysis or machine learning.

Section 1: Introduction To NumPy

Details of Section 1

1.1 What is the NumPy Python library?
1.2 What are NumPy arrays?
1.3 How to print the shape of a NumPy array?
1.4 How to access NumPy array elements?
1.5 How to reshape a NumPy array?
1.6 How to create a NumPy array using linspace in Python?
1.7 How to join two or more NumPy arrays?
1.8 How to load data from a text file using numpy.loadtxt?
1.9 How to load data from a text file using numpy.genfromtxt?
1.10 How to create a NumPy array filled with all zeroes or all ones?
1.11 How to create a NumPy array filled with a specific number?
1.12 How to create a NumPy array filled with random numbers?
1.13 How to combine NumPy arrays using vertical stack?
1.14 How to combine NumPy arrays using horizontal stack?

Section 2: Basic Vector Operations using Python NumPy

Details of Section 2

2.1 How to create a row vector and a column vector using Python NumPy?
2.2 How to create a zero vector using Python NumPy?
2.3 How to calculate the transpose of a vector using Python NumPy?
2.4 How to perform vector addition and subtraction using Python NumPy?
2.5 Perform vector and scalar multiplication using Python NumPy
2.6 How to calculate vector dot products using Python NumPy?
2.7 What is Cauchy-Schwarz inequality?
2.8 How to perform an outer product of vectors using Python NumPy?
2.9 How to perform the cross product using Python NumPy?
2.10 What is a unit vector?

Section 3: Matrix And Its Types

Details of Section 3

Section 4: Basic Matrix Operations

Details of Section 4

4.1 How to add two matrices using Python NumPy?
4.2 Calculate the transpose of a matrix using Python NumPy
4.3 How to perform matrix scalar multiplication using Python NumPy?
How to perform matrix-vector multiplication using Python NumPy?
4.4 How to perform matrix multiplication using Python NumPy?
4.5 How to calculate the Hadamard product using Python NumPy?
4.6 Calculate the trace of a matrix using Python NumPy
4.7 How to calculate the Frobenius inner product of two matrices using Python NumPy?

Section 5: Vector and Matrix Norms

Details of Section 5

5.1 How to calculate the L1 norm of a vector using Python?
5.2 How to calculate the L2 norm of a vector using Python?
5.3 How to calculate the max norm of a vector using Python?
5.4 How to calculate the Frobenius norm of a matrix using Python?
5.5 How to calculate the Euclidean distance between two matrices using Python?

Section 6: Matrix Rank

Details of Section 6

6.1 How to calculate the rank of a matrix using Python?

Section 7: Echelon Form of Matrices

Details of Section 7

7.1 What is the row echelon form of a matrix?
7.2 What are the pivots of a matrix?
7.3 How to calculate the reduced row echelon form of a matrix using Python?

Section 8: Determinants

Details of Section 8

8.1 Calculate the determinant of a matrix using Python NumPy
8.2 What is the characteristic polynomial of a matrix?

Section 9: Matrix Inverse

Details of Section 9

9.1 Calculate the inverse of a matrix using Python NumPy
9.2 Calculate the pseudoinverse of a matrix using Python

Section 10: QR Decomposition of Matrices

Details of Section 10

10.1 How to check whether a matrix is an orthogonal matrix using Python?
10.2 Perform QR decomposition of a matrix using Python
10.3 Calculate inverse of a matrix using QR decomposition in Python

Section 11: Eigen Decomposition

Details of Section 11

11.1 What are eigenvalues and eigenvectors?
11.2 How to calculate eigenvalues and eigenvectors using Python?
11.3 Eigen decomposition of a square matrix

Section 12: Singular Value Decomposition

Details of Section 12

12.1 Singular Value Decomposition (SVD) using Python

Section 13: Tensors

Details of Section 13

13.1 How to create a tensor using Python?
13.2 Perform tensor addition and subtraction using Python
13.3 Tensor Hadamard Product using Python

Section 14: Cholesky Decomposition

Details of Section 14

14.1 Cholesky decomposition using Python

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