Linear Algebra for Data Science | Data Science Summer School 2023

How can we run operations and analysis on large quantity of data? We need matrices to represent these data, process the network structure and learning operations to mine for insights. Linear Algebra is an essential branch of mathematics to help make running algorithms on massive datasets feasible. This workshop will help you to develop an understanding in this important branch of mathematics for data science.

[faisalIqbal_AI]

00:19 Data Science Summer School aims to open up scientific learning for the general public.
02:51 Importance of Data Science in Various Fields
08:38 Importance of Linear Algebra in Data Science
11:15 Solving system of linear equations and representing them in Matrix form.
17:12 Neural networks use matrices for image classification
19:48 Understanding Matrix Multiplication and Dot Product
25:35 Understanding linear combination and matrix products
28:17 Matrix multiplication has various applications and different dimensions of output.
33:46 Technique to prove matrix multiplication properties
36:21 Identity and diagonal matrices defined
42:20 Matrix Multiplication Example
45:37 Properties of Symmetric and Anti-symmetric Matrices
51:19 Trade of Matrices and Norms in Data Science
54:01 Exploring Different Norms in Data Science
59:48 Understanding linear dependence and rank in matrices
1:02:27 Linear dependence and independence for dimensionality reduction
1:07:44 Invertible matrices have specific properties and conditions.
1:10:05 Determinant definition and recursive formula explained
1:15:25 Determinants describe how area changes with linear transformations.
1:18:06 Determinant properties and calculations
1:23:17 Introduction to defining vectors in Python using NumPy
1:27:15 Introduction to basic linear algebra operations
1:32:29 Introduction to Eigen Decomposition in Data Science
1:43:39 Introduction to Eigenvalues and Eigenvectors
1:55:47 Eigenvectors and eigenvalues properties
1:58:38 Eigen decomposition and diagonalizable matrices
2:05:07 Finding eigenvalues and eigenvectors using matrix multiplication
2:09:30 Calculation of eigenvalues and eigenvectors for Matrices Lambda 1, 2, and 3
2:15:12 Solving systems of equations using linear algebra
2:18:03 Understanding characteristic polynomial and eigenvalues
2:23:19 Finding coefficients for lambda equal to zero
2:26:19 Finding determinant using characteristic polynomial
2:31:54 Explaining eigenvalues and eigenvectors in linear algebra.
2:34:43 Eigenvectors and unitary matrices
2:41:06 Singular Value Decomposition (SVD) involves eigen decomposition of a transpose a or a a transposed.
2:43:56 Eigenvectors and eigenvalues explained
2:50:23 Understanding Singular Value Decomposition (SVD)
2:53:59 Multiplying a matrix by 4 in SVD affects eigenvalues and transpose
3:00:26 Explaining the calculation of pseudo inverse
3:03:59 Eigenvalues and eigenvectors computation
3:11:53 Substituting eigenvalues and eigenvectors in matrices for linear algebra calculations
3:14:51 Implementing eigen decomposition in numpy for data analysis
3:21:06 Calculate covariance matrix, eigenvalues, eigenvectors, plot original data and eigenvectors
3:23:56 Covariance matrix helps in finding important directions in the data.
3:30:35 Discussion on nearest neighbor transformation
3:33:17 Plotting the Iris dataset and implementing Euclidean distance for data points.
3:39:03 Implementing K Nearest Neighbors algorithm for data classification
3:43:11 Evaluating the accuracy of the K-nearest neighbors method
4:00:00 Introduction to Linear Algebra in Data Science

[homlhnu]

the best tutorial for Data science. thanks

[abrilgonzalez]

Can we find the "calculus" and "statistics sand probability theory" material in your youtube channel?
Thanks you

[yulfgql]

Can you surjection to me which university working on Linear algebra with AI.