Math 0-1: Linear Algebra for Data Science & Machine Learning

  • Welcome
  • Introduction and Outline
Introduction and Outline
09:30
How to Succeed in this Course
08:45
Where to get the code
02:06
How to Take this Course
02:05
Lines and Planes
10:14
2 Equations and 2 Unknowns
12:58
3 Equations and 3 Unknowns
17:23
Gaussian Elimination
22:48
No Solutions
05:10
Infinitely Many Solutions
08:22
Review Summary
03:59
Suggestion Box
03:10
What is a Vector?
20:05
Adding and Subtracting Vectors
12:12
Dot Product
15:56
Dot Product (pt 2)
09:06
Dot Product Exercises in Python
17:49
Bonus Application: Neural Embeddings, Cosine Similarity (Optional)
21:36
Exercise: Normalizing a Vector
08:02
Exercise: The Vector Normal to a Plane
05:09
What is a Matrix?
27:59
Matrix Addition and Scalar Multiplication
03:52
Matrix Multiplication
18:02
Properties of Matrix Multiplication
08:19
Matrix-Vector Product
12:53
Application: Neural Networks
07:28
Element-Wise Product
03:23
Outer Product
09:50
Bonus Application: Replicating GPT-4
07:11
Matrix Exercises in Python
24:08
Linear Systems Revisited
06:19
Vectors and Matrices Summary
10:41
Identity Matrix
06:01
Diagonal Matrices
08:48
Matrix Inverse
24:20
Exercise: Inverse of the Inverse
07:59
Singular Matrices
08:14
Matrix Transpose
18:38
Properties of the Matrix Transpose
25:11
Symmetric Matrices
07:53
Transpose in Higher Dimensions
13:51
Orthogonal and Orthonormal Matrices and Vectors
14:27
Exercise: Orthogonal Matrices
03:21
Exercise: Inverse of a Product
02:25
Exercise: Transpose of Inverse of Symmetric Matrix
04:02
Exercise: Why Are Orthogonal Matrices Length- and Angle-Preserving?
09:26
Determinants (pt 1)
18:50
Determinants (pt 2)
23:09
Determinant Formula (Optional)
12:05
Determinant Identities (Optional)
06:01
Exercise: Determinant of a Unitary Matrix
02:23
Matrix Trace (Optional)
07:36
Positive Definite and Negative Definite Matrices
23:37
Exercise: Inverse of a Positive Definite Matrix
03:50
Exercise: Complete the Square
21:12
Matrix Operations Exercises in Python
13:56
Matrix Operations and Special Matrices Summary
11:35
Linear Independence and Dependence
34:31
Geometric Interpretation of Linear Combinations
07:46
The Rank of a Matrix
20:17
Matrix Decompositions (SVD, QR, LU, Cholesky)
24:50
Rank After Multplication
22:37
Low-Rank Approximations and Frobenius Norm
13:25
Applications: Recommender Systems and Topic Modeling (Optional)
17:09
Applications of SVD: Data Visualization and Feature Selection (Optional)
11:57
Bonus Application: LoRA for Diffusion Models and LLMs
09:14
Exercise: Generating a Positive Semi-Definite Matrix
05:15
Relationship Between Rank and Positive Definiteness
07:31
Matrix Decompositions in Python
20:09
Matrix Rank and Decompositions Summary
05:05
How to Find Eigenvalues and Eigenvectors (pt 1)
24:04
How to Find Eigenvalues and Eigenvectors (pt 2)
03:04
Exercise: Rotation Matrix
21:38
Exercise: Why Do A^TA and AA^T Have the Same Eigenvalues?
02:53
Exercise: Eigenvalues of the Inverse
02:48
Conjugate Transpose and Hermitian Matrices
11:31
Hermitian Matrices Have Real Eigenvalues
06:39
Diagonalization
24:11
Why Do Hermitian Matrices Have Orthogonal Eigenvectors?
06:29
Test for Positive Definiteness Using Eigenvalues
08:18
Determinant From Eigenvalues
03:02
Invertibility From Eigenvalues (Positive Definite Matrices Are Invertible)
04:54
Constructing the SVD ('Proof' of SVD)
26:00
Matrix Powers
08:30
Application: The Vanishing Gradient Problem
08:16
Functions of Matrices (Optional)
13:45
Eigenvalues in Python
25:16
Quiz: Square Root of a Matrix
05:50
Eigenvalues and Eigenvectors Summary
11:16
What is the Appendix?
03:47
Pre-Installation Check
04:13
Anaconda Environment Setup
20:21
How to install Numpy, Scipy, Matplotlib, Pandas, PyTorch, and TensorFlow
17:33
How to use Github & Extra Coding Tips (Optional)
11:12
Math Order for Machine Learning & Data Science
16:20
Can YouTube Teach Me Calculus? (Optional)
15:08
Is this for Beginners or Experts? Academic or Practical? Fast or slow-paced?
22:05
What order should I take your courses in? (part 1)
11:19
What order should I take your courses in? (part 2)
16:07
Where to get discount coupons and FREE deep learning material
05:49
Introduction and Outline
09:30
How to Succeed in this Course
08:45
Where to get the code
02:06
How to Take this Course
02:05
Lines and Planes
10:14
2 Equations and 2 Unknowns
12:58
3 Equations and 3 Unknowns
17:23
Gaussian Elimination
22:48
No Solutions
05:10
Infinitely Many Solutions
08:22
Review Summary
03:59
Suggestion Box
03:10
What is a Vector?
20:05
Adding and Subtracting Vectors
12:12
Dot Product
15:56
Dot Product (pt 2)
09:06
Dot Product Exercises in Python
17:49
Bonus Application: Neural Embeddings, Cosine Similarity (Optional)
21:36
Exercise: Normalizing a Vector
08:02
Exercise: The Vector Normal to a Plane
05:09
What is a Matrix?
27:59
Matrix Addition and Scalar Multiplication
03:52
Matrix Multiplication
18:02
Properties of Matrix Multiplication
08:19
Matrix-Vector Product
12:53
Application: Neural Networks
07:28
Element-Wise Product
03:23
Outer Product
09:50
Bonus Application: Replicating GPT-4
07:11
Matrix Exercises in Python
24:08
Linear Systems Revisited
06:19
Vectors and Matrices Summary
10:41
Identity Matrix
06:01
Diagonal Matrices
08:48
Matrix Inverse
24:20
Exercise: Inverse of the Inverse
07:59
Singular Matrices
08:14
Matrix Transpose
18:38
Properties of the Matrix Transpose
25:11
Symmetric Matrices
07:53
Transpose in Higher Dimensions
13:51
Orthogonal and Orthonormal Matrices and Vectors
14:27
Exercise: Orthogonal Matrices
03:21
Exercise: Inverse of a Product
02:25
Exercise: Transpose of Inverse of Symmetric Matrix
04:02
Exercise: Why Are Orthogonal Matrices Length- and Angle-Preserving?
09:26
Determinants (pt 1)
18:50
Determinants (pt 2)
23:09
Determinant Formula (Optional)
12:05
Determinant Identities (Optional)
06:01
Exercise: Determinant of a Unitary Matrix
02:23
Matrix Trace (Optional)
07:36
Positive Definite and Negative Definite Matrices
23:37
Exercise: Inverse of a Positive Definite Matrix
03:50
Exercise: Complete the Square
21:12
Matrix Operations Exercises in Python
13:56
Matrix Operations and Special Matrices Summary
11:35
Linear Independence and Dependence
34:31
Geometric Interpretation of Linear Combinations
07:46
The Rank of a Matrix
20:17
Matrix Decompositions (SVD, QR, LU, Cholesky)
24:50
Rank After Multplication
22:37
Low-Rank Approximations and Frobenius Norm
13:25
Applications: Recommender Systems and Topic Modeling (Optional)
17:09
Applications of SVD: Data Visualization and Feature Selection (Optional)
11:57
Bonus Application: LoRA for Diffusion Models and LLMs
09:14
Exercise: Generating a Positive Semi-Definite Matrix
05:15
Relationship Between Rank and Positive Definiteness
07:31
Matrix Decompositions in Python
20:09
Matrix Rank and Decompositions Summary
05:05
How to Find Eigenvalues and Eigenvectors (pt 1)
24:04
How to Find Eigenvalues and Eigenvectors (pt 2)
03:04
Exercise: Rotation Matrix
21:38
Exercise: Why Do A^TA and AA^T Have the Same Eigenvalues?
02:53
Exercise: Eigenvalues of the Inverse
02:48
Conjugate Transpose and Hermitian Matrices
11:31
Hermitian Matrices Have Real Eigenvalues
06:39
Diagonalization
24:11
Why Do Hermitian Matrices Have Orthogonal Eigenvectors?
06:29
Test for Positive Definiteness Using Eigenvalues
08:18
Determinant From Eigenvalues
03:02
Invertibility From Eigenvalues (Positive Definite Matrices Are Invertible)
04:54
Constructing the SVD ('Proof' of SVD)
26:00
Matrix Powers
08:30
Application: The Vanishing Gradient Problem
08:16
Functions of Matrices (Optional)
13:45
Eigenvalues in Python
25:16
Quiz: Square Root of a Matrix
05:50
Eigenvalues and Eigenvectors Summary
11:16
What is the Appendix?
03:47
Pre-Installation Check
04:13
Anaconda Environment Setup
20:21
How to install Numpy, Scipy, Matplotlib, Pandas, PyTorch, and TensorFlow
17:33
How to use Github & Extra Coding Tips (Optional)
11:12
Math Order for Machine Learning & Data Science
16:20
Can YouTube Teach Me Calculus? (Optional)
15:08
Is this for Beginners or Experts? Academic or Practical? Fast or slow-paced?
22:05
What order should I take your courses in? (part 1)
11:19
What order should I take your courses in? (part 2)
16:07
Where to get discount coupons and FREE deep learning material
05:49

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