Linear Algebra for Data Science and Machine Learning

Learn the fundamentals of Linear Algebra and apply them to Artificial Intelligence and Data Science

What you'll learn
- Understand the importance of Linear Algebra for Data Science and Machine Learning
- Explore fundamental concepts like scalars, vectors, matrices, and tensors
- Represent data and solve linear systems using algebraic methods
- Identify key properties and perform essential operations with vectors and matrices
- Master linear transformations (e.g., scaling, rotation, shearing)
- Compute eigenvectors, eigenvalues, and apply matrix decompositions (Eigendecomposition, SVD)
- Implement Principal Component Analysis (PCA) for dimensionality reduction
- Code Linear Algebra operations in Python using specialized libraries (e.g., NumPy, SciPy)
- Apply Linear Algebra to real-world Machine Learning applications
- Reinforce learning through theoretical exercises and hands-on challenges

Requirements
- Basic Python knowledge (data structures, functions, and array manipulation)
- Foundational math skills (core operations and equation manipulation)
- No prior advanced Linear Algebra experience required

Description
Linear Algebra is one of the essential foundations for anyone who wants to work in Data Science and Artificial Intelligence. Whether manipulating large datasets, building predictive models, or implementing Machine Learning algorithms, a solid understanding of this mathematical field is indispensable. This course is designed to provide an intuitive and practical approach to the most important concepts, combining theory and Python implementations to ensure you learn by applying.

The course is divided into six sections, each covering a fundamental aspect of Linear Algebra. We begin with an introduction to core concepts, explaining the importance of this discipline and how it connects to Data Science and Machine Learning. Here, we cover elements like scalars, vectors, matrices, and tensors, along with setting up the necessary Python libraries. We also explore data representation and how linear systems are used to solve mathematical problems.

In the second section, we dive deeper into vectors—their properties and applications. Vectors are fundamental components in data manipulation, feature scaling, and even defining the multidimensional spaces used in predictive models. You’ll learn about norms, unit vectors, orthogonal and orthonormal vectors, and visualize these structures intuitively through graphs.

Next, we explore matrices, which are widely used to represent data and process large volumes of information. We’ll cover key matrix properties, norms, transposition, inversion, and essential decompositions for diverse applications. These concepts are critical for neural networks, linear regressions, and dimensionality reduction techniques.

The fourth section focuses on operations involving vectors and matrices. We’ll study matrix multiplication, dot and cross products, reduction operations, and the cosine rule—essential tools for calculating data similarity and efficiently manipulating mathematical structures.

Then, we tackle linear transformations, a key concept for many advanced Machine Learning applications. We’ll examine how matrices enable operations like reflection, scaling, rotation, and shearing, while introducing eigenvectors, eigenvalues, and matrix decompositions. Techniques like Eigendecomposition, Singular Value Decomposition (SVD), and Principal Component Analysis (PCA) are explored here—indispensable tools for data compression and redundancy removal in learning models.

Finally, the sixth section isentirely dedicated to practical applications of Linear Algebra in Data Science and AI. We’ll implement linear systems, explore how neural networks leverage these mathematical concepts, dive deeper into Eigendecomposition and SVD, and apply PCA for analysis and dimensionality reduction. We’ll also work with techniques to measure similarity in structured data, ensuring you can use this knowledge to solve real-world problems. The section concludes with exercises to reinforce your learning.

By the end of this course, you’ll have a strong command of Linear Algebra applied to Data Science and Machine Learning—mastering not just the theory but also its implementation in Python. If you aim to build a rigorous mathematical foundation for professional work in AI and data, this course is an essential step in your journey.

Who this course is for:
- Data Science, Machine Learning and AI professionals and students looking to strengthen their mathematical foundations
- Developers and programmers seeking to understand and apply Linear Algebra in Python
- Researchers and academics interested in the mathematical principles behind neural networks and AI algorithms
- Data engineers and analysts who need to manipulate, transform and reduce dimensionality in datasets
- Anyone wanting to understand the mathematical fundamentals of AI and apply them in practical ways
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