Talk:Determinant

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Right handed coordinante

the following sentence is not clear. "The determinant of a set of vectors is positive if the vectors form a right-handed coordinate system, and negative if left-handed." what does "right-handed coordinate system" means? the "coordinate system" article does not mention it. amit man

Possible to do/see also items

linear algebra/analytic geometry

linear independence/collinearity, Gram determinant, tensor, positive definite matrix (Sylvester's criterion), defining a plane, Line-line intersection, Cayley–Hamilton_theorem, cross product, Matrix representation of conic sections, adjugate matrix, similar matrix have same det (Similarity invariance), Cauchy–Binet formula, Trilinear_coordinates, Trace diagram, Pfaffian

types of matrices

special linear group, special orthogonal group, special unitary group, indefinite special orthogonal group, modular group, unimodular matrix, matrices with multidimensional indices

number theory/algebra

Pell's equation/continued fraction?, discriminant, Minkowski's theorem/lattice, Partition_(number_theory), resultant, field norm, Dirichlet's_unit_theorem, discriminant of an algebraic number field

geometry, analysis

conformal map?, Gauss curvature, orientability, Integration by substitution, Wronskian, invariant theory, Monge–Ampère equation, Brascamp–Lieb_inequality, Liouville's formula, absolute value of cx numbers and quaternions (see 3-sphere), distance geometry (Cayley–Menger determinant), Delaunay_triangulation

open questions

Jacobian conjecture, Hadamard's maximal determinant problem

algorithms

polar decomposition, QR decomposition, Dodgson_condensation, Matrix_determinant_lemma, eigendecomposition a few papers: Monte carlo for sparse matrices, approximation of det of large matrices, The Permutation Algorithm for Non-Sparse Matrix Determinant in Symbolic Computation, DETERMINANT APPROXIMATIONS

examples

reflection matrix, Rotation matrix, Vandermonde matrix, Circulant matrix, Hessian matrix (Blob_detection#The_determinant_of_the_Hessian), block matrix, Gram determinant, Elementary_matrix, Orr–Sommerfeld_equation, det of Cartan matrix

generalizations

Hyperdeterminant, Quasideterminant, Continuant (mathematics), Immanant of a matrix, permanent, Pseudo-determinant, det's of infinite matrices / regularized det / functional determinant (see also operator theory), Fredholm determinant, superdeterminant

other

Determinantal point process, Kirchhoff's theorem,

books

[1]

Decomposition Methods

The article in general seems to be packed full of overly complicated ways of doing simple things. For instance the Decomposition Methods section fails to mention Gaussian Elimination (yes, it is mentioned in the Further Methods section). It makes no sense to me (so either I don't understand or the section is simply wrong) that det(A) = e*det(L)*det(U) given that det(A) = det(L') = det(U') for the upper triangular matrix U' and the lower triangular matrix L' that are EASILY arrived at (order O ~ n^3) by Gaussian Elimination. In other words, given how easy and efficient Gaussian Elimination is, LU Decomposition, etc. should be clearly justified here, and it is (they are) not. I also note the Wiki-article on Gaussian Elimination claims right up front that it operates on Rows of a matrix. This is just WRONG, it can operate on either Rows or Columns and if memory serves me (it may not) it can operate on both. Restricting discussion to row reduction is nonsense. Anyway, my main point is why should LU decomposition be mentioned here if it is MORE EXPENSIVE than Gaussian Elimination? Before discussing its details, that needs to be addressed - since as far as I can see it is only useful for reasons other than calculation of the determinant of a matrix.98.21.212.196 (talk) 22:55, 27 May 2017 (UTC)

-- umm, dude, the usual LU decomposition *is* gaussian elimination - U is the resulting row echelon form, L contains the sequence of pivot multipliers used during the elimination procedure. Which, btw, is generally done on rows because the RHS of a set of simultaneous equations - used to augment a matrix to solve those equations, which was the whole *point* of gaussian elimination - adds one or more additional columns (not rows), so the corresponding elimination procedure must act on rows. — Preceding unsigned comment added by 174.24.230.124 (talk) 06:26, 1 June 2017 (UTC)

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