This course aims to introduce learners to the fundamental concepts of linear algebra. By the end of the course, students will be able to understand systems of linear equations, perform elementary row operations, work with matrices and vectors, find inverses of matrices, decompose matrices using LU decomposition and QR decomposition, and solve linear systems using various methods such as Ordinary Least Squares. The course utilizes a combination of tutorials, examples, and practical problem-solving using programming languages like Julia and Python. This course is suitable for beginners interested in developing a strong foundation in linear algebra concepts and applications.
Overview
Syllabus
Mathematics vlog.
Systems of linear equations.
Systems of linear equations with infinite and with no solutions.
Elementary row operations.
Matrix addition.
Matrix multiplication.
Introduction to vectors.
Vector addition.
Unit vectors.
Dot product of two vectors.
Vector cross product.
Matrix vector multiplication.
Identity matrices.
Inverse matrices.
Finding the inverse of a 2x2 matrix.
Column view of a matrix.
Elementary matrices.
LU decomposition of matrices.
Transpose of matrices.
Vector spaces and subspaces.
Column space of a matrix.
Spanning a subspace.
Null space of a matrix.
Null space of a matrix example.
Null space examples.
Tutorial on points and vectors in linear algebra.
Tutorial on vector arithmetic in linear algebra.
Example problems on points and vectors in linear algebra.
Introduction to Euclidean vector spaces with Julia.
Tutorial on matrices with help from Julia.
Solving linear systems using elementary row operations with Julia.
Ordinary Least Squares Tutorial using Python.
Gram Schmidt process for QR decomposition using Julia.
Taught by
Dr Juan Klopper
