# Essential Linear Algebra for Data Science

Are you eager to delve into the world of Data Science but struggling with the required mathematical knowledge? This course, offered by the University of Colorado Boulder, is designed to equip you with essential Linear Algebra skills necessary for a successful career in Data Science. With a focus on practical applications rather than complex proofs, this course offers an express route to understanding fundamental concepts.

Throughout the course, you will:

• Get a comprehensive understanding of matrices and their application in solving real-world problems
• Explore n-dimensional space and transformations within it
• Gain insights into the key properties of linear systems, such as independence, basis, and rank
• Master projections in lower and higher dimensions for practical problem-solving

Upon completion, you will be well-prepared to tackle Statistical Modeling for Data Science Application, a crucial component of the University of Colorado Boulder's Master of Science in Data Science program.

Certificate Available ✔

##### Course Modules

This course includes modules covering Linear Systems and Gaussian Elimination, Matrix Algebra, Properties of a Linear System, Determinant and Eigens, as well as Projections and Least Squares.

#### Linear Systems and Gaussian Elimination

The Linear Systems and Gaussian Elimination module introduces you to the course, defining linear systems and exploring three solution options, coordinate system visualization, and the rules of Gaussian Elimination. Through practical examples, you'll gain a solid understanding of solving linear systems and Gaussian Elimination, preparing you for real-world problem-solving scenarios.

#### Matrix Algebra

The Matrix Algebra module delves into the essentials of matrix algebra, covering topics such as matrix multiplication, the identity matrix, and scale. You'll also have the opportunity to test your knowledge through quizzes, ensuring a comprehensive understanding of these fundamental concepts.

#### Properties of a Linear System

The Properties of a Linear System module delves into vectors, coordinates, linear combinations, spans, linear independence, linear transformations, and matrix inverses. Through examples and quizzes, you'll gain a profound understanding of these crucial concepts, setting the stage for advanced applications in data science.

#### Determinant and Eigens

The Determinant and Eigens module provides an in-depth exploration of determinants, inverses of matrices, eigenvalues, and eigenvectors. By mastering these concepts, you'll be well-equipped to analyze and manipulate data using advanced linear algebra techniques.

#### Projections and Least Squares

The Projections and Least Squares module covers transpose, inner product, unit vectors, orthogonal vectors, orthogonal projections, and least squares. Through practical examples and a final exam, you'll solidify your understanding of these concepts, preparing you for real-world data science challenges.

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