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Linear Algebra Basics
YOUR PATHWAY TO SUCCESS
This 5-day course provides a foundational understanding of linear algebra concepts essential for data science, machine learning, and computer graphics. Participants will explore vectors, matrices, linear transformations, systems of linear equations, eigenvalues, and eigenvectors.
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Course Duration
5 Days
Course Details
his 5-day course provides a foundational understanding of linear algebra concepts essential for data science, machine learning, and computer graphics. Participants will explore vectors, matrices, linear transformations, systems of linear equations, eigenvalues, and eigenvectors. The course emphasizes practical applications and problem-solving, using real-world examples to illustrate the importance of linear algebra in various fields. Through interactive sessions and hands-on exercises, learners will develop a strong grasp of linear algebra principles and be prepared for more advanced topics.
This course focuses on building intuition and understanding the geometric interpretations of linear algebra concepts. It covers matrix operations, including addition, multiplication, and inversion, and their applications in solving systems of equations and performing data transformations. The course also introduces the concept of vector spaces and subspaces, which are fundamental to understanding machine learning algorithms. By the end of this course, participants will be able to apply linear algebra techniques to solve practical problems and have the mathematical foundation for further study in related areas.
y the end of this course, learners will be able to:
- Understand vectors and vector operations.
- Perform matrix operations.
- Solve systems of linear equations.
- Understand linear transformations.
- Calculate eigenvalues and eigenvectors.
- Apply linear algebra concepts to real-world problems.
- Students and professionals in data science, machine learning, and computer graphics.
- Individuals who want to gain a solid understanding of linear algebra.
- Anyone who needs to use linear algebra in their work or studies.
Course Outline
5 days Course
- Introduction to Vectors and Vector Spaces:
- Vectors in 2D and 3D space.
- Vector operations: Addition, scalar multiplication, dot product, cross product.
- Geometric interpretation of vectors and vector operations.
- Vector spaces and subspaces.
- Practical exercise: Working with vectors and performing vector operations.
- Matrices and Matrix Operations:
- Matrices: Definition, dimensions, and types.
- Matrix operations: Addition, subtraction, multiplication, transpose, inverse.
- Matrix representation of linear transformations.
- Practical exercise: Performing matrix operations and representing linear transformations.
- Systems of Linear Equations:
- Systems of linear equations: Representation and solutions.
- Gaussian elimination and row reduction.
- Matrix methods for solving systems of equations.
- Applications of systems of equations.
- Practical exercise: Solving systems of linear equations using different methods.
- Systems of Linear Equations:
- Linear Transformations:
- Linear transformations: Definition and properties.
- Matrix representation of linear transformations.
- Composition of linear transformations.
- Change of basis.
- Practical exercise: Working with linear transformations and their matrix representations.
- Linear Transformations:
- Eigenvalues and Eigenvectors:
- Eigenvalues and eigenvectors: Definition and calculation.
- Applications of eigenvalues and eigenvectors: Data analysis, stability analysis.
- Diagonalization of matrices.
- Practical exercise: Calculating eigenvalues and eigenvectors and applying them to real-world problems.
- Eigenvalues and Eigenvectors:
