Determinant of matrices, eigenvalues and eigenvectors
Determinants, eigenvalues, eigenvectors: geometric meaning, finding methods, and linear transformation essence.
Linear-Algebra
Span, basis, and dimension
Linear independence, span, basis, dimension: fundamental concepts for vector spaces and subspaces.
The four fundamental subspaces in Linear Algebra
Four fundamental subspaces: row space, column space, nullspace, left nullspace with dimensions and relationships.
Solving Ax = b
Solving Ax=b: conditions for solutions, complete solution (particular + nullspace), rank relationships.
Nullspace and solving Ax=0
Nullspace and solving Ax=0: special solutions, free variables, reduced row echelon form.
Echelon Form and Rank of a matrix
Echelon form and matrix rank: row elimination, leading elements, and solving linear systems.
Vector spaces and subspaces
Vector spaces, subspaces, column space: 8 axioms, subspace properties, and linear combinations.
Basic concepts in Linear Algebra
Intro to linear algebra: scalars, vectors, norms, matrices, transpose, and linear combinations.