# Linear Algebra Concept

A Linear Algebra Concept is a mathematical concept for linear algebra domain.

**Context:**- It can (typically) be the referent of a Linear Algebra Term.
- It can (typically) be expressed in a Mathematical Language.
- It includes the study of linear sets of equations and their transformation properties which allows the analysis of rotation, translation and scaling in space.
- It also includes study of least squares fitting and solution of coupled differential equations.

**Example(s):****Counter-Example(s):****See:**Linear Programming Concept, Linear Algebra Textbook.

## References

### 2015

- http://wikipedia.org/wiki/List_of_linear_algebra_topics
- (0,1)-matrix; 2 × 2 real matrices; Adjugate; Affine coordinate system; Affine geometry; Affine group; Affine space; Affine transformation; Antihermitian matrix; Basis; Basis transformation matrix; Block matrix; Cartesian coordinate system; Category of vector spaces; Cauchy–Binet formula; Cayley–Hamilton theorem; Change of basis; Characteristic polynomial; Cholesky decomposition; Circulant matrix; Classical treatment of tensors; Clifford algebra; Column space; Component-free treatment of tensors; Conjugate transpose; Cramer's rule; Cyclic decomposition theorem; Cyclic subspace; Determinant; Diagonal matrix; Diagonalizable matrix; Dimension theorem for vector spaces; Dot product; Dual space; Eigenvalue, eigenvector and eigenspace; Elementary row operations; Euclidean group; Euclidean space; Examples of vector spaces; Exterior algebra; Flat (geometry); Galilean group; Galilean transformation; Gaussian elimination; Gauss–Jordan elimination; Geometric algebra; Glossary of tensor theory; Gram–Schmidt process; Hamel basis; Hamel dimension; Hankel matrix; Haynsworth inertia additivity formula; Hermitian matrix; Hessenberg matrix; Hessian matrix; Higher-order singular value decomposition; Householder transformation; Improper rotation; Indefinite orthogonal group; Inner product space; Intermediate treatment of tensors; Jordan normal form; LU decomposition; Least squares; Linear combination; Linear equation; Linear function; Linear functional; Linear independence; Linear map; Linear span; Linear subspace; List of matrices; Lorentz transformation; Matrices; Matrix theory; Matrix addition; Matrix congruence; Matrix consimilarity; Matrix decomposition; Matrix equivalence; Matrix inversion; Matrix multiplication; Matrix similarity; Minor; Multilinear algebra; Normed vector space; Null space; Null vector; Nullity theorem; Orientation (geometry); Orthogonal complement; Orthogonal group; Orthogonal matrix; Orthogonal projection; Orthogonality; Outer product; Perron–Frobenius theorem; Pfaffian; Poincaré group; Polar decomposition; Positive-definite; Projection; Projective geometry; Projective linear group; Projective space; Projective transformation; Pseudo-Euclidean space; Pseudoinverse; QR decomposition; Quadric; Rank; Rank-nullity theorem; Row and column spaces; Row equivalence; Row space; Scalar multiplication; Schur complement; Schur decomposition; Shear mapping; Singular value decomposition; Skew-symmetric matrix; Sparse matrix; Spectral theorem; Spread of a matrix; Squeeze mapping; Stochastic matrix; Strassen algorithm; Symmetric algebra; Symmetric matrix; Symplectic structure; System of linear equations; Tensor algebra; Tensor; Toeplitz matrix; Topological vector space; Trace; Transpose; Triangular matrix; Tridiagonal matrix; Unitary matrix; Vandermonde matrix; Vector space; Weyr canonical form; Woodbury matrix identity; conic section; invertible matrix; linear algebra; linear least squares; main diagonal; nullity; positive-semidefinite matrix;

### 2011

- Mark V. Sapir http://www.math.vanderbilt.edu/~msapir/msapir/list.html
- QUOTE: Algebraic system; An inversion in a permutation; Augmented matrix of a system of lin. equations; Back-substitution; Cofactor expansion along a row (column); Cofactor of entry aij; Column space of a matrix; Column-vector; Coordinates of a vector in a given basis; Coordinates of an n-vector; Core of a set of vectors; Cramer's rule; Determinant of a square matrix; Diagonal matrices; Distance between two vectors; Distance from a vector to a set in a Euclidean vector space; [[Dot product (Euclidean inner product) of n-vectors]]; Dot product (inner product) of functions; Eigenvector and eigenvalue of a linear operator; Eigenvector and eigenvalue of a matrix; Elementary matrix; Entry of a matrix; Equality of matrices; Euclidean vector space; Even and odd permutations; Free unknown; Gauss-Jordan elimination procedure; General linear operator; General linear transformations; General solution of a system of linear equations; Gram-Schmidt procedure; Homogenious system of lin. equations; Identity matrix; Identity operator; Injective maps; Inverse of a matrix; Invertible matrix; Kernel of a linear transformation; Leading 1 in a row echelon matrix; Leading unknown; Linear combination of vectors; Linear equation; Linear operator on Rn; Linear transformation from Rn to Rm; Linearly dependent sets of elements in a vector space; Linearly independent sets of elements in a vector space; Matrix of coefficients of a system of equations; Minor of entry aij; Multiplying a matrix by a scalar; Norm of a vector; Normal component of a vector; Null transformation; Operations on systems of linear equations; Orthogonal basis; Orthogonal complement of a subspace; Orthogonal vectors; Product of a row-vecror and a column-vector; Product of matrices; Projection of a vector onto a subspace; Properties of dot product; Range of a linear transformation; Rank of a set of vectors; Reduced row-echelon form; Row operations on matrices; Row-echelon form; Row-vector; Scalar; Sign of a permutation; Similar matrices; Size of a matrix; Skew-symmetric matrices; Solution of a linear equation; Solution of a system of linear equations; Square matrix; Standard matrix of a linear transformation; Subspace of a vector space; Sum of matrices; Surjective maps; Symmetric matrices; System of linear equations; The Wronskian of a set of functions; The adjoint of a matrix; The characteristic polynomial of a matrix; The dimension of a vector space; The inverse of an elementary matrix; The matrix of a linear operator; The null space of a matrix; The product of linear transformations; The sum of linear transformations; Trace of a matrix; Transpose of a matrix; Triangle; Lower-triangular matrix; Vector space spanned by a set of vectors; Vector space; Zero matrix; basis of a vector space; consistent system of equations; least squares solution of a system of linear equations; n-space; n-vector; transition matrix; transposition;