Talk:Determinant

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Right handed coordinante[edit]

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[edit]

linear algebra/analytic geometry[edit]

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[edit]

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

number theory/algebra[edit]

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[edit]

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[edit]

Jacobian conjecture, Hadamard's maximal determinant problem

algorithms[edit]

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[edit]

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[edit]

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[edit]

Determinantal point process, Kirchhoff's theorem,

books[edit]

[1]

Bad English[edit]

The lede (2nd sentence) states:"It [the determinant] can be computed from the entries of the matrix by a specific arithmetic expression, while other ways to determine its value exist as well." I have a couple of problems with this. The easiest one is whether or not the "other ways" clause is in any way useful or meaningful. (You can "determine" its value by inspection or comparison, but these seem so obvious as to not be helpful.) The second problem I see is the phrase "a specific arithmetic expression". An expression doesn't compute anything. (One USES the expression to compute...) Worse, there IS no "specific" expression (depending on what is meant by the term) which concretely and specifically expresses all additions & multiplications required for all matrices (of any size). The specific expression depends on the number of elements in the matrix under consideration. Isn't the term 'algorithm' better here? There is a GENERAL 'algorithm' which can be used to compute the value of any determinant, although there are many more efficient special case algorthims also. I also wonder whether the determinant is (as claimed in the first sentence of the Lede) a value? It certainly is if the matrix is composed of numbers - but what if it is composed of vectors? functions? operators? (any abstract mathematical object)? There are also matrices which are composed of more than one type of object (for instance both a set of variables variable and their numerical coefficients in some set of linear equations). Although these are generalizations of the definition of what a basic matrix is, not allowing the generalizations to enter into the explantion is equivalent to claiming, in an explanation of numbers, that they are (all) integers.173.189.76.20 (talk) 15:11, 13 August 2014 (UTC)

Geometric interpretation section[edit]

I have temporarily hidden this newly added section because it is a)poorly written b)not geometric in nature c)very trivial and d)unsourced and likely to be WP:OR. I could be wrong, so I didn't just delete it. Other opinions? Bill Cherowitzo (talk) 03:04, 11 September 2014 (UTC)

Agreed. It could have been intended as a geometric interpretation of specific properties of the determinant, but it got the illustrations wrong, and in any event would add little of value. The impression one gets is that the article is being treated as a sandbox to develop ideas in the absence of a source. —Quondum 06:13, 11 September 2014 (UTC)