Linear Algebra

Linear Algebra is the subtopic of algebra that deals exclusively with linear combinations of variables, including systems of linear equations, vector spaces, and linear transformations, often utilizing matrix algebra to streamline calculation.

Linear Equations & Matrices

  • Systems of Linear Equations
  • Matrices
  • Elementary Row Operations
  • Matrix Algebra
  • Gaussian Elimination

Matrix Properties

  • Linear Dependence & Independence
  • Invertible Matrices
  • Elementary Matrices
  • Determinants
  • Cramer's Rule
  • The Invertible Matrix Theorem

Vector Spaces

  • Vector Spaces
  • Vector Subspaces
  • Dimensions, Rank
  • Nullity
  • Row Space, Column Space

Bases

  • Spanning Sets
  • Basis
  • Change of Basis

Linear Transformations

  • Linear Transformations
  • Kernel & Range
  • Properties & Proofs

Eigenspaces

  • Eigenvalues
  • Eigenvectors
  • Diagonalization