# 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

### 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]

## Symbol / Convention confusing?

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)

|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.