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.
Get Instant Notification of New Courses on our
Telegram channel.
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.
Introduction
Introduction
Vectors – Introduction
Scalar vs. Vector
Vectors Fundamentals
Vectors – Magnitude and Direction
Magnitude and Direction – Introduction
Magnitude and Direction – Example 1
Magnitude and Direction – Example 2
Vectors – Properties
Properties – Introduction
Properties – Example 1
Properties – Example 2
Properties – Example 3
Vectors – Unit Vectors
Unit Vectors – Introduction
Unit Vectors – Example
Vectors – 3D Vectors
3D Vectors – Introduction
3D Vectors – Example
Vectors – Collinearity in Vectors
Collinearity in Vectors – Introduction
Collinearity in Vectors – Example 1
Collinearity in Vectors – Example 2
Collinearity in Vectors – Example 3
Collinearity in Vectors – Example 4
Vectors – Dot Product
Dot Product – Introduction
Dot Product – Example 1
Dot Product – Example 2
Dot Product – Example 3
Vectors – Dot Product Uses
Dot Product Uses – Introduction
Dot Product Uses – Example 1
Dot Product Uses – Example 2
Dot Product Uses – Example 3
Vectors – Cross Product
Cross Product – Introduction
Cross Product – Example
Vectors – Vectors Differentiation
Vectors Differentiation – Introduction
Vectors Differentiation – Example 1
Vectors Differentiation – Example 2
Vectors Differentiation – Example 3
Vectors Differentiation – Example 4
Vectors – Vectors Partial Differentiation
Vectors Partial Differentiation – Introduction
Vectors Partial Differentiation – Example
Vectors – Vectors Integration
Vectors Integration – Introduction
Vectors Integration – Example 1
Vectors Integration – Example 2
Vectors Integration – Path Integrals
Vectors – Vectors Double Integration
Vectors Double Integration – Introduction
Vectors Double Integration – Example
Vectors – Scalar Fields and Vector Fields
Scalar Fields vs. Vector Fields
Scalar Field Gradient – Introduction
Scalar Field Gradient – Example
Scalar Field Laplacian – Introduction
Scalar Field Laplacian – Example
Vector Filed Divergence – Introduction
Vector Filed Divergence – Example
Vector Filed Curl – Introduction
Vector Filed Curl – Example
Vector Field Laplacian – Introduction
Vector Field Laplacian – Example
Matrices – Introduction
Matrices Fundamentals
Matrices Rules – Introduction
Matrices Rules – Example 1
Matrices Rules – Example 2
Matrices – Commutator
Commutator – Introduction
Commutator – Example
Matrices – Matrix Operations
Matrix Operations – Introduction
Matrix Trace – Introduction
Matrix Trace – Example 1
Matrix Trace – Example 2
Matrix Transpose – Introduction
Matrix Transpose – Example
Matrix Complex Conjugate – Introduction
Matrix Complex Conjugate – Example
Matrix Hermitian Complex Conjugate – Introduction
Matrix Hermitian Complex Conjugate – Example
Matrices – Matrix Determinant
Matrix Determinant – Introduction
Matrix Determinant – Properties
Matrix Determinant – Example 1
Matrix Determinant – Example 2
Matrices – Matrix Inverse
Matrix Inverse – Introduction
Matrix Inverse – Example
Matrix Inverse – Matrix Inverse to Solve Algebraic Equations
Matrices – Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors – Introduction
Eigenvalues and Eigenvectors – Example
Matrices – Matrix Diagonalization
Matrix Diagonalization – Introduction
Matrix Diagonalization – Example 1
Matrix Diagonalization – Example 2
Matrix Diagonalization – Example 3
Tensors – Introduction
Tensors – Introduction
Tensors – Covariant vs. Contravariant Tensors
Tensors – Tensors Addition
Tensors Addition – Introduction
Tensors Addition – Example
Tensors – Tensors Contraction
Tensors Contraction – Introduction
Tensors Contraction – Example 1 (Dot Product)
Tensors Contraction – Example 2 (Trace)
Tensors – Tensors Expansion
Tensors Expansion – Tensors Multiplication (Dyad Product) – Introduction
Tensors Expansion – Tensors Multiplication (Dyad Product) – Example
