List of Linear Algebra Topics - Vector Spaces

Vector Spaces

  • Basis
    • Change of basis
    • Hamel basis
  • Dimension theorem for vector spaces
    • Hamel dimension
  • Examples of vector spaces
  • Linear map
    • Shear mapping or Galilean transformation
    • Squeeze mapping or Lorentz transformation
  • Column space
  • Row space
  • Null space, nullity
  • Rank-nullity theorem
  • Nullity theorem
  • Dual space
    • Linear function
    • Linear functional
  • Orthogonality
  • Orthogonal complement
  • Orthogonal projection
  • Outer product
  • Improper rotation
  • Category of vector spaces
  • Linear subspace
    • Euclidean subspace
  • Normed vector space
  • Inner product space

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    Surely, we are provided with senses as well fitted to penetrate the spaces of the real, the substantial, the eternal, as these outward are to penetrate the material universe. Veias, Menu, Zoroaster, Socrates, Christ, Shakespeare, Swedenborg,—these are some of our astronomers.
    Henry David Thoreau (1817–1862)