Simplified lecture note for linear algebra

This is a collection of simplified lecture notes for my linear algebra course. This collection contains minimum amount of information and is not intend to replace the textbook or lectures themselves.

• Linear systems
  • Basics of linear systems
  • Augmented matrices and elementary row operations
  • Linear systems with no solutions or infinitely many solutions
• Algebra of vectors
• Matrices
  • Basics of matrices
  • Matrices, linear systems, and linear transformations
  • Matrix products
  • Matrix inverse
  • 2x2 matrix determinant
  • 3x3 matrix determinant
  • General matrix determinant
  • Computing inverse via row reduction
• Vector spaces
  • Span and linear independence
  • Row space, column space, and matrix rank
  • Subspace of the Euclidean vector spaces
  • Null space
  • Basis and dimension

Please note that this collection of notes is intentionally written to not follow the typical “definition-lemma-theorem” structure, and thus differ from the adopted textbook significantly in terms of the structure.