the algebraic representation of geometric concepts in n-dimensional space. Fearnley-Sander (1979) describes Grassmann's foundation of linear algebra as...

In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever...

article focuses on matrices related to linear algebra, and, unless otherwise specified, all matrices represent linear maps or may be viewed as such. Square...

linear operator contains information about the operator's eigenvalues. The minimal polynomial of an algebraic element records the simplest algebraic relation...

polynomial algebras are used for the study of algebraic varieties, which are solution sets of systems of polynomial equations. Weyl algebras and Lie algebras may...

approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph...

mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector...

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

In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors)...

In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a rescaling followed...

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...

Hogben, L, ed. (2007). Handbook of Linear Algebra.[page needed] Arthur, John W. (2011). Understanding Geometric Algebra for Electromagnetic Theory. IEEE...

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

rotations, linear momentum as the generator of translations, electric charge being the generator of the U(1) symmetry group of electromagnetism, the color charges...

Addison-Wesley Secondary Math: An Integrated Approach: Focus on Algebra is an 812-page-long algebra textbook published in 1996. The lead authors are Randall...

Numerical methods used in scientific computation, for example numerical linear algebra and numerical solution of partial differential equations Stochastic...

those transformations whose linear part has determinant 1 is the group of orientation- and volume-preserving maps. Algebraically, this group is a semidirect...

6365. Nelson, Jelani; Nguyen, Huy L. (2013). OSNAP: Faster numerical linear algebra algorithms via sparser subspace embeddings. FOCS '13. arXiv:1211.1002...

] {\displaystyle {\begin{bmatrix}1&2&3\\a&b&c\\x&y&z\end{bmatrix}}} LinearAlgebra:-Determinant(M); b z − c y + 3 a y − 2 a z + 2 x c − 3 x b {\displaystyle...

In linear algebra and matroid theory, Rota's basis conjecture is an unproven conjecture concerning rearrangements of bases, named after Gian-Carlo Rota...

Lipschutz, Seymour (2001), Schaum's outline of theory and problems of linear algebra, New York: McGraw-Hill, pp. 69–80, ISBN 978-0-07-136200-9 Press, WH;...

along with 4×4 matrix support. These are distinct from more general linear algebra libraries in other domains focussing on matrices of arbitrary size....

ES) for graphics processing. Since "recent mathematical treatments of linear algebra and related fields invariably treat vectors as columns," designer Mark...

function fields. Algebraic structures occur as both discrete examples and continuous examples. Discrete algebras include: Boolean algebra used in logic gates...

composed of different spectral power distributions can be algebraically related to one another in a color matching context. Discovered by Hermann Grassmann these...

In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol or Levi-Civita epsilon represents a...

relations, discovered by W. R. Hamilton, also generate the quaternions as an algebra over the real numbers. Another presentation of Q8 is Q 8 = ⟨ a , b ∣ a...

theory). Continuous group theory, Lie algebras and differential geometry are used to understand the structure of linear and nonlinear partial differential...

new colors are linear combinations of the old colors. In short, the simplified language introduced before is not gauge invariant. Color charge is conserved...

Springer-Verlag, ISBN 978-0-387-40510-0, MR 2014408. Lay, David (2003), Linear Algebra and Its Applications, Addison-Wesley, ISBN 978-0-201-70970-4. Mac Lane...