Talk:Determinant
Determinant has been listed as a level4 vital article in Mathematics. If you can improve it, please do. This article has been rated as BClass. 
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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 righthanded coordinate system, and negative if lefthanded." what does "righthanded 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, Lineline 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 3sphere), 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 NonSparse 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, Pseudodeterminant, 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]
Geometric explanation for 2x2 matrices
I would like to precise only the following part of the explanation:
"yet it may be expressed more conveniently using the cosine of the complementary angle to a perpendicular vector, e.g. a^{⊥} = (b, a), such that a^{⊥}bcosθ' , which can be determined by the pattern of the scalar product to be equal to ad − bc"
As far as I understand it, for the scalar product to be ad − bc the vector a^{⊥} must be (b, a). So I would change "to a perpendicular vector, e.g." by "to the perpendicular vector". Actually, would that be the case, the module of a and a^{⊥} are the same, so the final expression could be better written in terms of a. Happy to do it, I would like just to confirm. Conjugado (talk) 00:52, 31 January 2018 (UTC)
Determinant identities
I suggest merging Determinant identities into this article. There's not enough there to justify a separate article. The original article creator was blocked a few times for creating inappropriate article fragments in the mainspace. Apocheir (talk) 21:26, 8 April 2018 (UTC)
I would be in mild, perichiral, agreement. Cuzkatzimhut (talk) 21:30, 8 April 2018 (UTC)