Linear algebra

Linear algebra is the branch of mathematics concerning linear equations, linear transformations (maps), and their representations in vector spaces and through matrices.

Vector Space

• Field
• Vector space
  • Subspace
• Linear combination
  • Span
• Linear independence
• Basis
  • Dimension
• Coordinates

Linear Transformation

• Linear transformation
• Isomorphism
• Fundamental theorem of linear algebra

Determinant

• Multilinear form
  • Alternating multilinear form
• Determinant
  • Properties of determinant
• Cramer’s rule

Characteristic Polynomial

Decomposition Theorems

Inner Product Space

• Inner product