Introducing Linear Algebra

Overview

Dive into the fundamentals of linear algebra through a comprehensive 9-hour mathematics vlog. Explore systems of linear equations, including those with infinite and no solutions, and master elementary row operations. Learn matrix operations like addition and multiplication, and delve into vector concepts such as addition, unit vectors, dot products, and cross products. Understand matrix-vector multiplication, identity matrices, and inverse matrices, including how to find the inverse of a 2x2 matrix. Examine the column view of matrices, elementary matrices, and LU decomposition. Study vector spaces, subspaces, column spaces, and null spaces with practical examples. Engage in tutorials on points, vectors, and vector arithmetic in linear algebra, and solve example problems. Gain hands-on experience using Julia for Euclidean vector spaces, matrices, and solving linear systems. Conclude with an Ordinary Least Squares tutorial using Python and learn the Gram-Schmidt process for QR decomposition using Julia.

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.