determinant (Q1420): Difference between revisions

@@ Property / topic's main category @@
+Category:Determinants
@@ Property / topic's main category: Category:Determinants / rank @@
+Normal rank
@@ Property / Freebase ID @@
+/m/02c2w
@@ Property / Freebase ID: /m/02c2w / rank @@
+Normal rank
@@ Property / Freebase ID: /m/02c2w / reference @@
+stated in: Freebase Data Dumps
publication date: 28 October 2013Timestamp +2013-10-28T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
-Timestamp
++2013-10-28T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
 After
@@ Property / subclass of @@
+invariant
@@ Property / subclass of: invariant / rank @@
+Normal rank
@@ Property / subclass of @@
+alternating multilinear map
@@ Property / subclass of: alternating multilinear map / rank @@
+Normal rank
@@ Property / Stack Exchange tag @@
+https://stackoverflow.com/tags/determinants
+Normal rank
@@ Property / PSH ID @@
@@ Property / PSH ID: 7275 / rank @@
+Normal rank
@@ Property / NDL Authority ID @@
+00562696
@@ Property / NDL Authority ID: 00562696 / rank @@
+Normal rank
@@ Property / NDL Authority ID: 00562696 / reference @@
+imported from Wikimedia project: Japanese Wikipedia
@@ Property / Library of Congress authority ID @@
+sh85037299
@@ Property / Library of Congress authority ID: sh85037299 / rank @@
+Normal rank
@@ Property / Library of Congress authority ID: sh85037299 / reference @@
+imported from Wikimedia project: Japanese Wikipedia
@@ Property / Bibliothèque nationale de France ID @@
+11975737s
@@ Property / Bibliothèque nationale de France ID: 11975737s / rank @@
+Normal rank
@@ Property / Bibliothèque nationale de France ID: 11975737s / reference @@
+imported from Wikimedia project: Japanese Wikipedia
@@ Property / MathWorld ID @@
+Determinant
@@ Property / MathWorld ID: Determinant / rank @@
+Normal rank
@@ Property / MathWorld ID: Determinant / reference @@
+imported from Wikimedia project: English Wikipedia
@@ Property / Commons category @@
+Determinant
@@ Property / Commons category: Determinant / rank @@
+Normal rank
@@ Property / defining formula @@
+ $\det({\boldsymbol {A}})=\sum _{\sigma \in S_{n}}\left(\operatorname {sgn}(\sigma )\prod _{i=1}^{n}a_{i,\sigma _{i}}\right)$ 
\det(\boldsymbol{A}) = \sum_{\sigma \in S_n} \left( \sgn(\sigma) \prod_{i=1}^n a_{i,\sigma_i}\right)
+Normal rank
@@ Property / Great Russian Encyclopedia Online ID (old version) @@
+2691291
@@ Property / Great Russian Encyclopedia Online ID (old version): 2691291 / rank @@
+Normal rank
+subject named as: ОПРЕДЕЛИТЕЛЬ
@@ Property / OpenMath ID @@
+linalg1#determinant
@@ Property / OpenMath ID: linalg1#determinant / rank @@
+Normal rank
@@ Property / Encyclopædia Britannica Online ID @@
+topic/determinant-mathematics
+Normal rank
+subject named as: determinant
@@ Property / Brilliant Wiki ID @@
+expansion-of-determinants
@@ Property / Brilliant Wiki ID: expansion-of-determinants / rank @@
+Normal rank
@@ Property / Australian Educational Vocabulary ID @@
+scot/15495
@@ Property / Australian Educational Vocabulary ID: scot/15495 / rank @@
+Normal rank
@@ Property / described by source @@
+New Encyclopedic Dictionary
@@ Property / described by source: New Encyclopedic Dictionary / rank @@
+Normal rank
@@ Property / described by source @@
+ISO 80000-2:2019 Quantities and units — Part 2: Mathematics
+Normal rank
+section, verse, paragraph, or clause: 2-16.10
+subject named as: determinant of matrix
@@ Property / described by source @@
+Brockhaus and Efron Encyclopedic Dictionary
+Normal rank
@@ Property / described by source @@
+Small Brockhaus and Efron Encyclopedic Dictionary
+Normal rank
@@ Property / described by source @@
+Encyclopædia Britannica 11th edition
@@ Property / described by source: Encyclopædia Britannica 11th edition / rank @@
+Normal rank
+statement is subject of: 1911 Encyclopædia Britannica/Determinant
@@ Property / Microsoft Academic ID @@
+158041659
@@ Property / Microsoft Academic ID: 158041659 / rank @@
+Normal rank
@@ Property / Microsoft Academic ID @@
+2778383128
@@ Property / Microsoft Academic ID: 2778383128 / rank @@
+Normal rank
@@ Property / YSO ID @@
@@ Property / YSO ID: 11285 / rank @@
+Normal rank
@@ Property / YSO ID: 11285 / reference @@
+stated in: YSO-Wikidata mapping project
@@ Property / definition domain @@
+square matrix
@@ Property / definition domain: square matrix / rank @@
+Normal rank
@@ Property / nLab ID @@
+determinant
@@ Property / nLab ID: determinant / rank @@
+Normal rank
@@ Property / studied in @@
+linear algebra
@@ Property / studied in: linear algebra / rank @@
+Normal rank
@@ Property / studied in @@
+Q1670
@@ Property / studied in: Q1670 / rank @@
+Normal rank
@@ Property / IEV number @@
+-06-20
@@ Property / IEV number: 102-06-20 / rank @@
+Normal rank
@@ Property / BNCF Thesaurus ID @@
@@ Property / BNCF Thesaurus ID: 32649 / rank @@
+Normal rank
@@ Property / BNCF Thesaurus ID: 32649 / qualifier @@
+subject named as: Determinanti
@@ Property / Zhihu topic ID @@
+19900291
@@ Property / Zhihu topic ID: 19900291 / rank @@
+Normal rank
@@ Property / Zhihu topic ID: 19900291 / qualifier @@
+subject named as: 行列式
@@ Property / image @@
+Schema sarrus-regel.png
@@ Property / image: Schema sarrus-regel.png / rank @@
+Normal rank
@@ Property / Online PWN Encyclopedia ID @@
+3999183
@@ Property / Online PWN Encyclopedia ID: 3999183 / rank @@
+Normal rank
@@ Property / National Library of Israel J9U ID @@
+987007550422505171
@@ Property / National Library of Israel J9U ID: 987007550422505171 / rank @@
+Normal rank
@@ Property / National Library of Israel J9U ID: 987007550422505171 / reference @@
+stated in: National Library of Israel
@@ Property / Store norske leksikon ID @@
+determinant
@@ Property / Store norske leksikon ID: determinant / rank @@
+Normal rank
@@ Property / Den Store Danske ID @@
+determinant
@@ Property / Den Store Danske ID: determinant / rank @@
+Normal rank
@@ Property / notation @@
+vertical bar brackets
@@ Property / notation: vertical bar brackets / rank @@
+Normal rank
@@ Property / NL CR AUT ID @@
+ph153485
@@ Property / NL CR AUT ID: ph153485 / rank @@
+Normal rank
@@ Property / NL CR AUT ID: ph153485 / qualifier @@
+subject named as: determinanty
@@ Property / Krugosvet article @@
+nauka_i_tehnika/matematika/OPREDELITEL.html
+Normal rank
@@ Property / on focus list of Wikimedia project @@
+Wikipedia:Vital articles/Level/4
+Normal rank
+point in time: 31 October 2022Timestamp +2022-10-31T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
-Timestamp
++2022-10-31T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
 After
@@ Property / GND ID @@
+4138983-9
@@ Property / GND ID: 4138983-9 / rank @@
+Normal rank
@@ Property / Encyclopedia of Mathematics article ID @@
+determinant
@@ Property / Encyclopedia of Mathematics article ID: determinant / rank @@
+Normal rank
@@ Property / Digital Library of Mathematical Functions ID @@
+.3.i
@@ Property / Digital Library of Mathematical Functions ID: 1.3.i / rank @@
+Normal rank
@@ Property / in defining formula @@
+ $\operatorname {sgn}()$ 
\sgn()
@@ Property / in defining formula: $\operatorname {sgn}()$ / rank @@
+Normal rank
@@ Property / in defining formula: $\operatorname {sgn}()$ / qualifier @@
+symbol represents: parity of a permutation
@@ Property / in defining formula @@
+ $\sum$ 
\sum
@@ Property / in defining formula: $\sum$ / rank @@
+Normal rank
@@ Property / in defining formula: $\sum$ / qualifier @@
+symbol represents: sum
@@ Property / in defining formula @@
+ $\prod$ 
\prod
@@ Property / in defining formula: $\prod$ / rank @@
+Normal rank
@@ Property / in defining formula: $\prod$ / qualifier @@
+symbol represents: product
@@ Property / in defining formula @@
+ $S_{n}$ 
S_n
@@ Property / in defining formula: $S_{n}$ / rank @@
+Normal rank
@@ Property / in defining formula: $S_{n}$ / qualifier @@
+symbol represents: symmetric group
@@ Property / in defining formula @@
+ $\sigma$ 
\sigma
@@ Property / in defining formula: $\sigma$ / rank @@
+Normal rank
@@ Property / in defining formula: $\sigma$ / qualifier @@
+symbol represents: permutation
@@ Property / in defining formula @@
+ ${\boldsymbol {A}}$ 
\boldsymbol{A}
@@ Property / in defining formula: ${\boldsymbol {A}}$ / rank @@
+Normal rank
@@ Property / in defining formula: ${\boldsymbol {A}}$ / qualifier @@
+symbol represents: square matrix
@@ Property / in defining formula @@
+ $\det({\boldsymbol {A}})$ 
\det(\boldsymbol{A})
@@ Property / in defining formula: $\det({\boldsymbol {A}})$ / rank @@
+Normal rank
@@ Property / in defining formula: $\det({\boldsymbol {A}})$ / qualifier @@
+symbol represents: determinant
@@ Property / ScienceDirect topic ID @@
+mathematics/det
@@ Property / ScienceDirect topic ID: mathematics/det / rank @@
+Normal rank
@@ Property / codomain @@
+set of complex numbers
@@ Property / codomain: set of complex numbers / rank @@
+Normal rank
@@ Property / Larousse ID @@
+divers/déterminant_dune_matrice_carrée_M_=_αij_dordre_n_sur_un_corps_K/42750
+Normal rank
@@ Property / Gran Enciclopèdia Catalana ID (former scheme) @@
+0267697
@@ Property / Gran Enciclopèdia Catalana ID (former scheme): 0267697 / rank @@
+Normal rank
@@ Property / Gran Enciclopèdia Catalana ID @@
+algebra-multilineal
@@ Property / Gran Enciclopèdia Catalana ID: algebra-multilineal / rank @@
+Normal rank
@@ Property / Metamath statement ID @@
+df-mdet
@@ Property / Metamath statement ID: df-mdet / rank @@
+Normal rank

Latest revision as of 16:05, 29 July 2024

sum of signed terms of n factors from n×n matrix with no two factors sharing row or column

matrix determinant
determinant of matrix
determinant of a square matrix

Language	Label	Description	Also known as
English	determinant	sum of signed terms of n factors from n×n matrix with no two factors sharing row or column	matrix determinant determinant of matrix determinant of a square matrix