Introducing Linear Algebra

This introductory course develops foundational linear algebra through systems of equations, matrices, vectors, vector spaces, and matrix decompositions. It includes practical examples using Julia and Python, including least squares and QR decomposition.

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.