In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix generated from A by removing one or more of its rows and columns...

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number...

is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector...

education Minor (graph theory), a relation of one graph to another Minor (matroid theory), a relation of one matroid to another Minor (linear algebra), the...

group and that of the subgroup Cofactor (linear algebra), the signed minor of a matrix Minor (linear algebra), an alternative name for the determinant...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

semisimple Lie algebra is a linear Lie algebra under the adjoint representation. This may lead to some ambiguity, as every Lie algebra is already linear with respect...

In linear algebra, an invertible matrix is a square matrix that has an inverse. In other words, if some other matrix is multiplied by the invertible matrix...

In mathematics, a linear algebraic group is a subgroup of the group of invertible n × n {\displaystyle n\times n} matrices (under matrix multiplication)...

In linear algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear...

a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a perfect field is...

are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field. The phrase group of Lie type does...

V\otimes V} to itself induces a linear automorphism that is called a braiding map. More generally and as usual (see tensor algebra), let V ⊗ n {\displaystyle...

Campbell, H: "Linear Algebra With Applications", pages 111–112. Appleton Century Crofts, 1971 Eves 1990, p. 405 A Brief History of Linear Algebra and Matrix...

In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues...

linear algebra, a principal axis is a certain line in a Euclidean space associated with a ellipsoid or hyperboloid, generalizing the major and minor axes...

geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is...

In linear algebra, a generalized eigenvector of an n × n {\displaystyle n\times n} matrix A {\displaystyle A} is a vector which satisfies certain criteria...

In linear algebra, a linear relation, or simply relation, between elements of a vector space or a module is a linear equation that has these elements...

{\displaystyle 2\times 3} ⁠. Matrices are commonly used in linear algebra, where they represent linear maps. In geometry, matrices are widely used for specifying...

finite-dimensional real Lie algebra is isomorphic to a matrix Lie algebra. Meanwhile, for every finite-dimensional matrix Lie algebra, there is a linear group (matrix...

In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of...

mathematician Élie Cartan. Amusingly, the Cartan matrices in the context of Lie algebras were first investigated by Wilhelm Killing, whereas the Killing form is...

(March–April 1989). "Sufficient matrices and the linear complementarity problem". Linear Algebra and Its Applications. 114–115: 231–249. doi:10...

matrix Tridiagonal matrix Invariant subspace Axler, Sheldon Jay (1997). Linear Algebra Done Right (2nd ed.). New York: Springer. pp. 86–87, 169. ISBN 0-387-22595-1...

In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃəˈlɛski/ shə-LES-kee) is a decomposition of a Hermitian, positive-definite...

In linear algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, major diagonal, or good diagonal) of a matrix A...

In linear algebra, the permanent of a square matrix is a function of the matrix similar to the determinant. The permanent, as well as the determinant,...

matrices of size 3 × 3 or larger. This can be shown by using the matrix's minors to calculate the determinant. Pickover, Clifford A. (2011), The Zen of Magic...

Sylvester, James Joseph (1851). "On the relation between the minor determinants of linearly equivalent quadratic functions". Philosophical Magazine. 1:...