Álgebra Linear com Python para Machine Learning e Modelagem

Explore the fundamentals of Linear Algebra with a practical, hands-on approach using Python. This course provides a clear and concise understanding of core concepts, demonstrating their application through real-world examples and code.

Key topics covered:

• Vectors: Dive into vector types and operations, essential building blocks of linear algebra.
• Matrices: Master matrix types, operations (addition, multiplication, transpose), and determinant calculations.
• Systems of Linear Equations: Learn various methods for solving linear systems, including:
  • Addition Method
  • Substitution Method
  • Cramer's Rule
  • Gaussian Elimination (Row Reduction)
• Laplace Theorem & Cofactors: Understand these important concepts for matrix manipulation.
• Least Squares Estimation: Discover how to find the best-fit solution for overdetermined systems.
• Multiple Linear Regression: Apply linear algebra to build and interpret multiple linear regression models.
• Linear Transformations: Explore various transformations like:
  • Homothety
  • Translation
  • Rotation
  • Reflection
  • Shear
  • Dilation & Contraction
  • Identity, Null, and Inverse Transformations
• Eigenvalues & Eigenvectors: Uncover the power of eigenvalues and eigenvectors.
• Principal Component Analysis (PCA): Learn how to reduce dimensionality and extract key features using PCA.

Practical Application:

The course utilizes real-world datasets to illustrate how linear algebra is applied to data analysis. You'll learn the initial data analysis steps and see how it connects to:

• Least Squares Method
• Multiple Linear Regression
• Principal Component Analysis (PCA)

Getting Started with Python & Google Colaboratory:

The first section provides a gentle introduction to Python and Google Colaboratory, ensuring a smooth learning experience even if you're new to these tools.

Accessibility:

This course is designed to be accessible on Windows using Google Colaboratory. Linux and Mac users can easily follow along using Jupyter Notebook.

Prepare to gain a new perspective on linear algebra and its powerful applications!