Your Gateway to Data Science and Machine Learning Essentials through Mastering Vectors, Matrices and Tensors.
Linear algebra isn’t just about calculations, it’s a powerful lens to see the world. This foundational course introduces university students to the core principles of linear algebra, offering a comprehensive exploration of fundamental concepts and applications. Designed to cultivate a strong mathematical framework, the curriculum spans key topics essential for understanding vector spaces, matrices, tensors and linear transformations. Students will delve into the mathematical structures that underpin these concepts, gaining proficiency in operations such as addition, multiplication, and inversion of matrices. The course places a significant emphasis on practical problem-solving, thus guiding students through the application of linear algebra in real-world scenarios, including computer graphics, optimization, data science and data analysis.
What you’ll learn
- Gain knowledge of vector spaces and calculations.
- Gain knowledge of matrix properties and operations.
- Gain knowledge of eigenvalues and eigenvectors.
- Gain knowledge of tensor properties and operations.
Course Content
- Introduction –> 1 lecture • 6min.
- Vectors – Introduction –> 2 lectures • 11min.
- Vectors – Magnitude and Direction –> 3 lectures • 10min.
- Vectors – Properties –> 4 lectures • 6min.
- Vectors – Bases –> 1 lecture • 9min.
- Vectors – Unit Vectors –> 2 lectures • 3min.
- Vectors – 3D Vectors –> 2 lectures • 7min.
- Vectors – Collinearity in Vectors –> 5 lectures • 11min.
- Vectors – Dot Product –> 4 lectures • 15min.
- Vectors – Dot Product Uses –> 4 lectures • 13min.
- Vectors – Cross Product –> 2 lectures • 15min.
- Vectors – Vectors Differentiation –> 5 lectures • 18min.
- Vectors – Vectors Partial Differentiation –> 2 lectures • 6min.
- Vectors – Vectors Integration –> 4 lectures • 23min.
- Vectors – Vectors Double Integration –> 2 lectures • 9min.
- Vectors – Scalar Fields and Vector Fields –> 11 lectures • 36min.
- Matrices – Introduction –> 4 lectures • 31min.
- Matrices – Commutator –> 2 lectures • 7min.
- Matrices – Matrix Operations –> 10 lectures • 26min.
- Matrices – Matrix Determinant –> 4 lectures • 25min.
- Matrices – Matrix Inverse –> 3 lectures • 23min.
- Matrices – Eigenvalues and Eigenvectors –> 2 lectures • 19min.
- Matrices – Matrix Diagonalization –> 4 lectures • 33min.
- Tensors – Introduction –> 2 lectures • 9min.
- Tensors – Tensors Addition –> 2 lectures • 2min.
- Tensors – Tensors Contraction –> 3 lectures • 4min.
- Tensors – Tensors Expansion –> 2 lectures • 4min.
Requirements
Linear algebra isn’t just about calculations, it’s a powerful lens to see the world. This foundational course introduces university students to the core principles of linear algebra, offering a comprehensive exploration of fundamental concepts and applications. Designed to cultivate a strong mathematical framework, the curriculum spans key topics essential for understanding vector spaces, matrices, tensors and linear transformations. Students will delve into the mathematical structures that underpin these concepts, gaining proficiency in operations such as addition, multiplication, and inversion of matrices. The course places a significant emphasis on practical problem-solving, thus guiding students through the application of linear algebra in real-world scenarios, including computer graphics, optimization, data science and data analysis.
The exploration of eigenvalues and eigenvectors forms a crucial component of the course, providing students with a deeper understanding of diagonalization and its diverse applications across disciplines. Through a combination of theoretical instruction and hands-on exercises, students will be able to develop analytical skills and critical thinking that allows them to approach complex problems with confidence.
Upon completion, students will possess a solid foundation in linear algebra, equipping them for advanced coursework in mathematics, computer science, physics, engineering, and various other fields where linear algebra plays a pivotal role.