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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
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
special linear group,
special orthogonal group,
special unitary group, indefinite special orthogonal group,
modular group,
unimodular matrix,
matrices with multidimensional indices
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
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
Jacobian conjecture, Hadamard's maximal determinant problem
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
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
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
Determinantal point process, Kirchhoff's theorem,
The Example about "In a triangular matrix, the product of the main diagonal is the determinant"
There are many triangular matrices which can be derived. Unless you state more constraints (e.g. Hermite Normal Form or alike), you cannot simply postulate that the diagonal product is the determinant. For example, if I produce some (remember - it is not unique) upper triangular matrix with row operations, instead of column operations, I cannot reproduce the findings in the example. So, either constraints or insights are clearly missing.
2003:E5:2709:8B91:29A5:FE96:3F33:E513 ( talk) 07:50, 4 August 2022 (UTC)
There are two mentions of "the linear map" associated to a matrix and one to "(the matrix of) a linear transformation". The word "the" in all of them is incorrect, since in each case noun referred to is not unique.
The first two occurrences should be replaced with "a". The last sentence is correct without the parenthesized clause, as a sentence about the determinant of a linear transformation. Alternatively the parenthesis can be adjusted to "a matrix representing". Thatwhichislearnt ( talk) 14:32, 28 February 2024 (UTC)
Sorry, I meant the text resulting from D.Lazard's edit of 17:24. I don't care whose text it is, it is superior to using just an indefinite article. The key point of matrices is that for a given choice of bases there is a 1-1 correspondence between linear transformations and matrices of appropriate size. That's where the definite article comes from. And please refrain from attacking another user; keep the discussion on the article. -- Elphion ( talk) 18:16, 28 February 2024 (UTC)
Look, I agree with D.Lazard that the definite article is superior; I agree with you that some reference to choice of bases is appropriate. And I repeat, casting shade on a fellow editor ("gaslighting" above) is not helpful, and will eventually get you blocked. -- Elphion ( talk) 19:06, 28 February 2024 (UTC)
The helpful way to proceed at this point is to suggest a concrete prospective wording here on the talk page so we can discuss it. -- Elphion ( talk) 19:20, 28 February 2024 (UTC)
This is the
talk page for discussing improvements to the
Determinant article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Find sources: Google ( books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
Archives: 1, 2, 3Auto-archiving period: 60 days |
This
level-4 vital article is rated B-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
Daily pageviews of this article
A graph should have been displayed here but
graphs are temporarily disabled. Until they are enabled again, visit the interactive graph at
pageviews.wmcloud.org |
This page has archives. Sections older than 60 days may be automatically archived by Lowercase sigmabot III when more than 4 sections are present. |
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
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
special linear group,
special orthogonal group,
special unitary group, indefinite special orthogonal group,
modular group,
unimodular matrix,
matrices with multidimensional indices
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
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
Jacobian conjecture, Hadamard's maximal determinant problem
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
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
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
Determinantal point process, Kirchhoff's theorem,
The Example about "In a triangular matrix, the product of the main diagonal is the determinant"
There are many triangular matrices which can be derived. Unless you state more constraints (e.g. Hermite Normal Form or alike), you cannot simply postulate that the diagonal product is the determinant. For example, if I produce some (remember - it is not unique) upper triangular matrix with row operations, instead of column operations, I cannot reproduce the findings in the example. So, either constraints or insights are clearly missing.
2003:E5:2709:8B91:29A5:FE96:3F33:E513 ( talk) 07:50, 4 August 2022 (UTC)
There are two mentions of "the linear map" associated to a matrix and one to "(the matrix of) a linear transformation". The word "the" in all of them is incorrect, since in each case noun referred to is not unique.
The first two occurrences should be replaced with "a". The last sentence is correct without the parenthesized clause, as a sentence about the determinant of a linear transformation. Alternatively the parenthesis can be adjusted to "a matrix representing". Thatwhichislearnt ( talk) 14:32, 28 February 2024 (UTC)
Sorry, I meant the text resulting from D.Lazard's edit of 17:24. I don't care whose text it is, it is superior to using just an indefinite article. The key point of matrices is that for a given choice of bases there is a 1-1 correspondence between linear transformations and matrices of appropriate size. That's where the definite article comes from. And please refrain from attacking another user; keep the discussion on the article. -- Elphion ( talk) 18:16, 28 February 2024 (UTC)
Look, I agree with D.Lazard that the definite article is superior; I agree with you that some reference to choice of bases is appropriate. And I repeat, casting shade on a fellow editor ("gaslighting" above) is not helpful, and will eventually get you blocked. -- Elphion ( talk) 19:06, 28 February 2024 (UTC)
The helpful way to proceed at this point is to suggest a concrete prospective wording here on the talk page so we can discuss it. -- Elphion ( talk) 19:20, 28 February 2024 (UTC)