# 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

### types of matrices

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

### 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

### 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

[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||b|cosθ' , which can be determined by the pattern of the scalar product to be equal to adbc"

As far as I understand it, for the scalar product to be adbc 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)