Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations in finite dimensions. Vector spaces are a central theme in modern mathematics; thus, linear algebra is widely used in both abstract algebra and functional analysis. Linear algebra also has a concrete representation in analytic geometry and it is generalised in operator theory. It has extensive applications in the natural sciences and the social sciences.

Subcategories

There are 5 subcategories to this category.

A

• Affine geometry

D

• Determinants

M

• Matrix theory
• Multilinear algebra

N

• Numerical linear algebra

Articles in category "Linear algebra"

There are 148 articles in this category.

(0,1)-matrix 3 3D projection A Adjacency matrix Affine space Affine transformation Antilinear B Balanced set Barycentric coordinates Basis (linear algebra) Biadjacency matrix Bidiagonal matrix C Category of graded vector spaces Category of vector spaces Cauchy-Binet formula Cayley-Hamilton theorem Change of bases Characteristic equation Characteristic polynomial Codimension Column vector Complex conjugate vector space Conformable Conjugate transpose Coordinate space Coordinates vector Cramer's rule Cross product D Delta operator Determinant Dimension Dimension (vector space) Dimension theorem for vector spaces Direct sum Dodgson condensation Dot product Dual basis in a field extension Dual space E Eigenplane Eigenvalue Eigenvector Elementary reflector Euclidean space Examples of vector spaces F Flag (linear algebra) Frobenius normal form Fundamental theorem of linear algebra G Gaussian elimination General linear group Generalized singular value decomposition

G cont. Graded vector space Gram-Schmidt process Gramian matrix H Hessenberg matrix Hilbert space Homogeneous co-ordinates Householder transformation I Identity matrix Invariant subspace Inverse iteration J Jordan normal form L LU decomposition Levi-Civita symbol Linear algebra Linear combination Linear complementarity problem Linear complex structure Linear functional Linear independence Linear least squares Linear span Linear subspace Linear system Linear transformation M Main diagonal Matrix (mathematics) Matrix addition Matrix inversion Matrix norm Matrix theory Multilinear algebra N Nilpotent matrix Norm (mathematics) Normal basis Null space Null vector (vector space) Nullity O Orientation (mathematics) Orthogonal complement Orthogonality Orthogonalization Orthonormality P Partial trace Permanent Perron-Frobenius theorem Pfaffian Polynomial basis Predual Projection (linear algebra) Projection operator

P cont. Pseudoinverse Q QR algorithm Quaternion Quotient space (linear algebra) R Rank (linear algebra) Rank-nullity theorem Rayleigh quotient Rayleigh quotient iteration Row and column spaces Row vector S SLERP Scalar Scalar multiplication Schur complement Self-adjoint Sesquilinear form Shear (mathematics) Similarity (mathematics) Singular Singular value decomposition Skew-symmetric matrix Spectral graph theory Spectral theorem Spectral theory Spectrum of an operator Squeeze mapping Standard basis Strassen algorithm Sublinear function Supertrace Sylvester's law of inertia Symplectic vector space System of linear equations T Tikhonov regularization Toeplitz matrix Trace (matrix) Transformation matrix Transpose Triangle inequality Triangular factor Triangular matrix U Unit vector Unitary matrix User:Trieu/Method of matrix rank V Vector (spatial) Vector space Vector space example 2 W Woodbury matrix identity Z Zech's logarithms