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Voit lisätä Alaindeksi- ja Yläindeksi-symbolit työkalupalkkiin.
where superscript T refers to the transpose operation, and [a
missä yläindeksi T tarkoittaa matriisin transpoosia ja [a
A superscript or subscript is a number, figure, symbol, or indicator that is smaller than the normal line of type and is set slightly above it (superscript) or below it (subscript).
Ala- tai yläindeksi on numero, kuva, merkki tai osoitin, joka on normaalia kirjasintekstiä pienempi ja hieman sen yläpuolella (yläindeksi) tai alapuolella (alaindeksi).
Auto-rotate Screen, Keep Screen on, Show/Hide Icons, Superscript Verse No's and others settings available.
Auto-Kierrä näyttöä, Keep Screen, Näytä / Piilota kuvakkeet, Yläindeksi Verse nro: n ja muut käytettävissä olevat asetukset.
The vector cross product also can be expressed as the product of a skew-symmetric matrix and a vector: a × b = × b = {\displaystyle \mathbf {a} \times \mathbf {b} =_{\times }\mathbf {b} ={\begin{bmatrix}\,0&\!-a_{3}&\,\,a_{2}\\\,\,a_{3}&0&\!-a_{1}\\-a_{2}&\,\,a_{1}&\,0\end{bmatrix}}{\begin{bmatrix}b_{1}\\b_{2}\\b_{3}\end{bmatrix}}} a × b = × T a = , {\displaystyle \mathbf {a} \times \mathbf {b} =_{\times }^{\mathrm {T} }\mathbf {a} ={\begin{bmatrix}\,0&\,\,b_{3}&\!-b_{2}\\-b_{3}&0&\,\,b_{1}\\\,\,b_{2}&\!-b_{1}&\,0\end{bmatrix}}{\begin{bmatrix}a_{1}\\a_{2}\\a_{3}\end{bmatrix}},} where superscript T refers to the transpose operation, and × is defined by: × = d e f . {\displaystyle _{\times }{\stackrel {\rm {def}}{=}}{\begin{bmatrix}\,\,0&\!-a_{3}&\,\,\,a_{2}\\\,\,\,a_{3}&0&\!-a_{1}\\\!-a_{2}&\,\,a_{1}&\,\,0\end{bmatrix}}.} The columns ×,i of the skew-symmetric matrix for a vector a can be also obtained by calculating the cross product with unit vectors, i.e.: × , i = a × e ^ i , i ∈ { 1 , 2 , 3 } {\displaystyle _{\times ,i}=\mathbf {a} \times \mathbf {{\hat {e}}_{i}} ,\;i\in \{1,2,3\}} or × = ∑ i = 1 3 ( a × e ^ i ) ⊗ e ^ i , {\displaystyle _{\times }=\sum _{i=1}^{3}(\mathbf {a} \times \mathbf {{\hat {e}}_{i}} )\otimes \mathbf {{\hat {e}}_{i}} ,} where ⊗ {\displaystyle \otimes } is the outer product operator.
Vektorien ristitulo voidaan ilmaista myös antisymmetrisen matriisin ja vektorin tulona: a × b = × b = {\displaystyle \mathbf {a} \times \mathbf {b} =_{\times }\mathbf {b} ={\begin{bmatrix}\,0&\!-a_{3}&\,\,a_{2}\\\,\,a_{3}&0&\!-a_{1}\\-a_{2}&\,\,a_{1}&\,0\end{bmatrix}}{\begin{bmatrix}b_{1}\\b_{2}\\b_{3}\end{bmatrix}}} a × b = × T a = {\displaystyle \mathbf {a} \times \mathbf {b} =_{\times }^{\mathrm {T} }\mathbf {a} ={\begin{bmatrix}\,0&\,\,b_{3}&\!-b_{2}\\-b_{3}&0&\,\,b_{1}\\\,\,b_{2}&\!-b_{1}&\,0\end{bmatrix}}{\begin{bmatrix}a_{1}\\a_{2}\\a_{3}\end{bmatrix}}} missä yläindeksi T tarkoittaa matriisin transpoosia ja × määritellään seuraavasti: × = d e f . {\displaystyle _{\times }{\stackrel {\rm {def}}{=}}{\begin{bmatrix}\,\,0&\!-a_{3}&\,\,\,a_{2}\\\,\,\,a_{3}&0&\!-a_{1}\\\!-a_{2}&\,\,a_{1}&\,\,0\end{bmatrix}}.} On huomattava, että × on kääntyvä matriisi, jossa a on sen oikean- tai vasemmanpuoleinen nollavektori.
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