Matrix Algebra

Dive into the fundamental concepts of matrix algebra in this comprehensive 3.5-hour tutorial. Learn essential topics such as matrix multiplication, including the ABBA method, and explore the properties of invertible matrices. Discover the importance of elementary matrices and their products, and master the LU factorization technique. Delve into subspaces, understanding their characteristics and how to identify them. Explore the concepts of span, nullspace, and column space, and their relationships to matrix properties. Gain a solid understanding of basis and dimension, including how to verify if a set of vectors forms a basis. Investigate coordinates and their significance in linear algebra. Examine the connections between nullspace, column space, and matrix rank. Venture into infinite dimensions and their implications. Finally, explore interesting applications like outer products and magic matrices, broadening your perspective on matrix algebra's practical uses.

Matrix Multiplication.
ABBA.
Inverse of matrix.
Invertible matrix.
Invertible matrices are square.
Elementary Matrix.
Product of elementary matrices.
LU factorization.
Subspace.
Not subspace.
Span is a subspace.
Nullspace of a matrix.
Nullspace is a subspace.
Basis and dimension.
Check something is a basis.
Coordinates.
Nullspace Column Space and Rank.
Infinite dimensions.
Outer Product.
Magic Matrix.