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]

Symbol / Convention confusing?[edit]

I'm not familiar with wikipedia formatting guidelines, but it is confusing to me that Matrices are A in text, but A in formulas. — Preceding unsigned comment added by 141.3.42.183 (talk) 18:21, 7 April 2015 (UTC)

Yeah, the font distinction is a little problematic. It is that, or sizing/placement problems. There is another intermediate format for inline use: A, which is used in some articles and should be more similar to the format in standalone formulae. —Quondum 23:51, 7 April 2015 (UTC)

Condense the lead[edit]

I propose a shorter, simpler, more concise, more user-friendly, more informative lead:

In linear algebra, the determinant is a useful value that can be computed from the elements of a square matrix. The determinant of a matrix A is denoted det(A), det A, or |A|.
In the case of a 2x2 matrix, the specific formula for the determinant is simply the upper left element times the lower right element, minus the product of the other two elements. Similarly, suppose we have a 3x3 matrix A, and we want the specific formula for its determinant |A|:
|A| = \begin{vmatrix} a & b & c\\d & e & f\\g & h & i \end{vmatrix} = a\begin{vmatrix} e & f\\h & i \end{vmatrix}-b\begin{vmatrix} d & f\\g & i \end{vmatrix}+c\begin{vmatrix} d & e\\g & h \end{vmatrix} = aei+bfg+cdh-ceg-bdi-afh.
Each of the 2x2 determinants in this equation is called a "minor". The same sort of procedure can be used to find the determinant of a 4x4 matrix, and so forth.
Any matrix has a unique inverse if its determinant is nonzero. Various properties can be proved, including that the determinant of a product of matrices is always equal to the product of determinants; and, the determinant of a Hermetian matrix is always real.
Determinants occur throughout mathematics. For example, a matrix is often used to represent the coefficients in a system of linear equations, and the determinant is used to solve those equations. The use of determinants in calculus includes the Jacobian determinant in the substitution rule for integrals of functions of several variables. Determinants are also used to define the characteristic polynomial of a matrix, which is essential for eigenvalue problems in linear algebra. Sometimes, determinants are used merely as a compact notation for expressions that would otherwise be unwieldy to write down.

Of course, wikilinks would be included as appropriate.Anythingyouwant (talk) 05:16, 3 May 2015 (UTC)

I went ahead and installed this.Anythingyouwant (talk) 19:46, 3 May 2015 (UTC)