Linear Algebra Crash Course - Mathematics for Machine Learning and Generative AI [Full 7h]

Unlock the power of linear algebra in this comprehensive 7-hour masterclass, essential for anyone aspiring to excel in AI, data science, and cutting-edge technologies. Dive deep into the core concepts and applications of linear algebra that are pivotal for mastering the mathematical foundations required in high-tech fields today.

If you want to learn complete - one semester equivalent Linear Algebra course check out
our comprehensive "Fundamentals to Linear Algebra 26+h course" as part of our LunarTech Unlimited Access plan, which will give you access to not just this but also other courses like Machine Learning, Data Science, and Deep Learning courses.

🔢🧠 Master the Math Behind Data Science and AI in 2024

This comprehensive roadmap introduces linear algebra concepts and techniques essential for building cutting-edge machine learning models.

Key Features:

📈 Structured Learning: Progress from foundational concepts to advanced techniques, including metric factorization and projections.
🚀 Practical Focus: Understand how linear algebra powers algorithms used in data science, AI, and generative AI.
🔮 2024 Relevance: Stay ahead of the curve with a roadmap tailored to the latest developments in the field.

Ideal For:

💡 Aspiring data scientists and AI professionals
💪 Anyone seeking to strengthen their grasp of the math behind machine learning

🚨 Launch Your Data Science Career with LunarTech.AI! 🚨

🎁 Free Resources:

🖥️ Resources and Courses to get into Machine Learning

👤 Meet Your Instructor: Tatev Aslanyan

🔔 Connect with Us:

[00:00:00] - Introduction to the course
[00:08:30] - Linear Algebra Roadmap for 2024
[00:27:50] - Course Prerequisites
[00:28:05] - Refreshment: Real Numbers and Vector Spaces
[00:31:18] - Refreshment: Norms and Euclidean Distance
[00:41:13] - Why These Prerequisites Matter
[00:45:00] - Foundations of Vectors
[00:50:00] - Vector - Geometric Representation Example
[01:15:51] - Special Vectors
[01:28:01] - Vector Application Example
[01:40:25] - Vectors Operations and Properties
[02:24:14] - Scalar Multiplication Application Example
[02:31:14] - Scaling Multiplication - Geometric Intuition
[02:39:31] - Dot Product, Geometric Interpretation, Examples
[03:06:00] - Understanding Dot Product and Similarity Measure
[03:24:00] - Cauchy Schwarz Inequality - Derivation & Proof
[03:37:00] - Introduction to Linear Systems and Matrices
[04:10:02] - Core Matrix Operations
[05:18:41] - Solving Linear Systems - Gaussian Elimination
[05:23:00] - Detailed Example - Solving Linear Systems
[05:45:46] - Detailed Example - Reduced Row Echelon Form (Augmented Matrix, REF, RREF)

#LinearAlgebra #LinearAlgebraCrashCourse #LinearAlgebraMasterclass #AIandDataScience #MathForTech #VectorMath #MatrixOperations #STEMEducation #TechInnovation2023 #FutureOfDataScience #MathematicalFoundations #AdvancedMathematics

[tx]

Thank you for After failing Maths in the 1970s, channels like yours have helped me to "have a go"—not for a career but to prevent cognitive decline. I may not understand it all, but that's okay; for me, just trying is important.

[ReflectionOcean]

By YouSum Live

00:00:00 Linear algebra fundamentals for AI and data science
00:01:50 Importance of mastering vectors in linear algebra
00:02:20 Applications of vectors in data science and AI
00:05:17 Solving linear systems using matrices and Gaussian elimination
00:10:40 Understanding determinants, inverses, and matrix transformations
00:20:01 Practical applications of matrix inverses in machine learning
00:20:51 Introduction to advanced linear algebra
00:20:59 Explore fundamental linear algebra topics
00:21:01 Understand vector spaces and projections
00:21:07 Dive into matrix factorization techniques
00:21:13 Learn about QR decomposition
00:21:15 Comprehend eigenvalue decomposition
00:21:27 Delve into singular value decomposition (SVD)
00:26:12 Grasp the concept of real numbers and vector spaces
00:30:26 Define norms and their significance
00:32:26 Differentiate between norm and Euclidean distance
00:40:24 Apply norms and Euclidean distance in machine learning
00:42:19 Emphasize the importance of prerequisites in understanding linear algebra
00:43:10 Linear algebra fundamentals for real-world applications
00:43:29 Mastering theory, examples, and must-know concepts
00:44:42 Efficient learning approach for practical application readiness
00:44:47 Foundations of vectors: theory, practice, and representation
00:45:10 Vectors: magnitude, direction, and common notations
00:45:56 Scalers vs. vectors: single numeric volume vs. magnitude-direction
00:50:16 Vector representation in 2D space: magnitude and direction
00:51:57 Pythagorean theorem for vector magnitude calculation
00:56:34 Common ways to represent vectors in different dimensional spaces
01:02:03 Vectors in n-dimensional space: notation and indexing
01:07:30 Understanding Vectors and Matrices
01:07:51 Defining vectors and matrices
01:09:10 Nested vectors and matrices
01:16:18 Special vectors: zero and unit vectors
01:19:00 Sparsity in vectors
01:28:18 Applications of vectors in word counting
01:30:42 Importance of word frequency in document analysis
01:31:20 Utilizing word counts for sentiment analysis
01:32:52 Stop words impact on document understanding
01:35:42 Application of word frequency in various contexts
01:36:35 Role of vectors in customer purchase representation
01:40:33 Vector addition and subtraction fundamentals
01:45:46 Generalization of vector addition and subtraction
01:53:22 Visualization of vector addition in a coordinate space
01:57:19 Introduction to vector addition properties
01:57:49 Commutative property: order of vectors doesn't matter
01:58:14 Associative property: order of addition doesn't affect result
01:58:52 Addition of zero vector has no impact
01:59:13 Subtracting a vector from itself results in zero vector
02:15:26 Scalar multiplication: scaling vector's magnitude
02:21:41 Effect of scalar multiplication by zero on any vector
02:24:31 Understanding scalar vector multiplication
02:25:01 Audio volume adjustment through scalar multiplication
02:26:04 Visualizing scalar multiplication in audio processing
02:32:02 Geometric interpretation of scaling vectors
02:40:30 Dot product's role in linear algebra
02:40:42 Dot product as a measure of vector extension
02:42:34 Dot product's relation to vector length
02:45:52 Applying Pythagorean theorem to vector lengths
02:48:01 Understanding the concept of dot product
02:49:04 Applying Pythagorean theorem to find vector length
02:50:21 Relating dot product to vector length
02:55:42 Generalizing dot product to n-dimensional vectors
02:56:50 Defining dot product for n-dimensional vectors
02:57:02 Explaining the concept of transpose in dot product
03:00:01 Calculating dot product for 3-dimensional vectors
03:06:00 Interpreting dot product as a measure of similarity
03:09:00 Applying cosine rule to understand dot product geometrically
03:13:06 Understanding the dot product concept
03:13:40 Recognizing the dot product as a distance measure
03:14:48 Applying dot product to vector lengths
03:20:38 Utilizing dot product for similarity calculations
03:23:24 Exploring inner product in abstract vector spaces
03:24:26 Understanding Cauchy-Schwarz inequality
03:30:40 Importance of Cauchy-Schwarz inequality in various fields
03:33:01 Significance of norm being zero in vectors
03:37:10 Introduction to matrices and linear systems
03:37:42 Introduction to linear systems in linear algebra
03:38:20 Linear systems enable efficient problem-solving in computing
03:38:30 Representation of general linear systems with M equations
03:39:01 Understanding the linear combination of vectors
03:41:20 Importance of systematic coefficient labeling in matrices
03:43:51 Differentiation between homogeneous and nonhomogeneous systems
03:54:00 Definition and structure of matrices in mathematics
04:04:12 Introduction to matrix dimensions
04:05:03 Understanding matrix structure and indices
04:05:29 Importance of matrix dimensions in mathematics
04:06:30 Significance of dimensions in data science
04:10:10 Matrix operations: addition, subtraction, scalar multiplication
04:11:13 Matrix addition: corresponding elements addition
04:12:16 Matrix subtraction: corresponding elements subtraction
04:13:08 Scalar multiplication of a matrix
04:23:01 Matrix multiplication: product of two matrices
04:29:12 Introduction to matrix multiplication
04:29:24 Matrix C obtained by multiplying matrices A and B
04:30:18 Dimension of matrix C determined by dimensions of A and B
04:31:32 Computing elements of matrix C using dot product
04:37:05 Detailed calculation example of matrix multiplication
04:44:36 Importance of solving linear systems with matrices
04:49:59 Applications of solving linear systems beyond mathematics
04:51:01 Linear systems representation and importance
04:53:44 Transformation of linear systems into matrices and vectors
04:54:11 Linear algebra application in solving systems of equations
04:54:24 Matrix representation compactly expresses linear systems
04:55:02 Understanding dimensions crucial for matrix operations
04:55:32 Introducing column vectors for efficient matrix multiplication
04:56:01 Transitioning linear equations into matrix-vector products
04:57:07 Consolidating equations into coefficient matrix and vector form
04:57:44 Simplifying system of equations using matrix notation
05:00:13 Importance of matrix notation for solving complex equations
05:17:52 Gaussian elimination method for systematic linear system solutions
05:18:51 Introduction to coefficient Matrix
05:19:00 Formation of argumented coefficient Matrix
05:20:29 Understanding dimensions of the new Matrix
05:22:32 Significance of argumented Matrix in solving equations
05:31:06 Transition to row Echelon form explanation
05:33:11 Definition and importance of reduced row Echelon form
05:35:52 Practical application through example problems
05:37:02 Step-by-step transformation into argumented Matrix
05:40:01 Gaussian elimination for row operations
05:44:50 Introduction to Gaussian elimination method
05:45:02 Eliminating elements to reach row echelon form
05:46:00 Using row operations to manipulate the matrix
05:49:19 Achieving zeros in specific positions
05:49:56 Transitioning to reduced row echelon form
05:57:02 Identifying unique solutions in reduced form
06:00:06 Explaining solutions in homogeneous and nonhomogeneous systems
06:01:15 Solving a system with unique solutions
06:09:19 Applying Gaussian elimination to a new system
06:12:30 Indications of infinite solutions in matrix operations
06:14:32 Transition from row echelon to reduced row echelon form
06:18:47 Expressing solutions as linear combinations of unknowns
06:25:00 Sponsorship message from Lunarch promoting tech education
06:26:41 Encouragement for innovation and leveraging AI's potential

By YouSum Live

[drkameldiab]

Love and Respect from Middle East ❤.. Thanks.. I learn From You ❤

[akshatpratapsingh]

Thank you very much for this crash course!

[SDRicky]

If I had a mathemtics teacher like that, I would love to do the class, even on Sunday.

[tech-adventurer]

It's a shame that you don't have like 100K likes. Excellent material!

[BugMateo]

Great content and detailed explanations, thanks. FYI: on 4:44:42 (Matrix Multiplication: Example 2) the result is [20, 36] [36, 68] ...not 66

[Hexzer]

great course thank you very much... just please try to change your equal sign, looks like a number two and it's confusing

[GuruPrasad-ispu]

Make videos on other mathematics topics like probability, statistics and calculas❤

[KumR]

Do we have something similar for Calculus, Statistics for probability....?

[backfromyourdream]

That's what I was looking for, thank you.

[deniscozma]

I m stupid in the math, but your courses motivated me to learn it ☺️.

[surkewrasoul]

Lovely tutorial, It would be even more interesting if the tutor was actually showing on the side of the video the whole time, So to make things more interactive. 😇

[waltenharesvilela]

Why did you choose yellow to write in the board? It is a bad choice, it is invisible.

[franklinbethel-jeym]

Please does LunarTech offer free courses ?

[DataEngineeringArabic]

Amazing course, this took me 20 years back when i was a university student in engineering faculty .
i have a question, i'm 41 years old, and i want to study Data science, do you think it is too late for me ? i just felt in love with this field and i believe i can do it, what do you think ? thank you

[okarakoo]

Thank you for the great course. If you do not mind a suggestion, try to improve your penmanship, which is frankly atrocious. Keep up the goof work!

[BablessBah-Ameen]

I am interested in meeting such not lucky yet to meet them....leave a contact or email for more communications....

[Arsonist]

4:44:38 calculation is not right. C22 is not 66 but 68. Give me free membership for figuring it out. I love your site but me poor.

[adenwhw]

the first 30 mins are wasting everybodys time coz if they know what you are talking about they don't need to learn