Introducing Linear Algebra
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. Read more