List of linear algebra topics

Linear equations

• System of linear equations
• Determinant
  • Minor (linear algebra)
• Cramer's rule
• Gauss-Jordan elimination

Matrices

• List of matrices, glossary of matrix theory
  • Stochastic matrix
  • Toeplitz matrix
• Matrix theory
• Matrix multiplication
• Characteristic polynomial
• Trace (matrix)
• Cayley-Hamilton theorem
• Eigenvalue, eigenvector
• Jordan normal form
• Rank (matrix theory)
• Matrix inversion
• Adjugate
• Transpose
  • Dot product
  • Symmetric matrix
  • Orthogonal matrix
  • Skew-symmetric matrix
  • Conjugate transpose
    • Unitary matrix
    • Hermitian matrix
• Positive definite, positive semidefinite
• Diagonal matrix, main diagonal
• Spectral theorem
• Decompositions
  • Cholesky decomposition
  • LU decomposition
  • Singular value decomposition
• Schur complement

Vectors

• Scalar multiplication
• Linear combination
• Linear span
• Linear independence
• Basis (linear algebra)

Vector spaces

• Dimension theorem for vector spaces
• Linear transformation
  • Galilean transformation, Lorentz transformation
• Column space
• Row space
• Null space, nullity
• Rank-nullity theorem
• Dual space
  • Linear function
  • Linear functional
• Orthogonality
• Category of vector spaces

Multilinear algebra

• Tensor
  • Classical treatment of tensors
  • Intermediate treatment of tensors
  • Component-free treatment of tensors

Affine space

• Affine transformation
• Affine group
• Affine geometry

Referenced By