math:2-14

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math:2-14 [2023/06/07 12:55] – [47.6.] rootmath:2-14 [2023/06/07 12:56] (текущий) – [47.7.] root
Строка 102: Строка 102:
 в базисе в базисе
  
-$(\widetilde{e_{1}},\widetilde{e_{2}})=(e_{1},e_{2})\left(\begin{array}{cc}+$$(\widetilde{e_{1}},\widetilde{e_{2}})=(e_{1},e_{2})\left(\begin{array}{cc}
 1 & 1\\ 1 & 1\\
 2 & 3 2 & 3
-\end{array}\right)$+\end{array}\right)$$
  
-$(e_{1},e_{2})=(\widetilde{e_{1}},\widetilde{e_{2}})\left(\begin{array}{cc}+$$(e_{1},e_{2})=(\widetilde{e_{1}},\widetilde{e_{2}})\left(\begin{array}{cc}
 1 & 1\\ 1 & 1\\
 2 & 3 2 & 3
Строка 113: Строка 113:
 3 & -1\\ 3 & -1\\
 -2 & 1 -2 & 1
-\end{array}\right)$+\end{array}\right)$$
  
-$(e^{1},e^{2})=(\widetilde{e^{1}},\widetilde{e^{2}})\left(\begin{array}{cc}+$$(e^{1},e^{2})=(\widetilde{e^{1}},\widetilde{e^{2}})\left(\begin{array}{cc}
 1 & 1\\ 1 & 1\\
 2 & 3 2 & 3
-\end{array}\right)$+\end{array}\right)$$
  
-$\widetilde{t_{jk}^{i}}=\left(\widetilde{e^{1}}+2\widetilde{e^{2}}\right)\otimes \left(\widetilde{e^{1}}+3\widetilde{e^{2}}\right)\otimes (3\widetilde{e_{1}}-2\widetilde{e_{2}}-\widetilde{e_{1}}+\widetilde{e_{2}})=\left(\widetilde{e^{1}}+2\widetilde{e^{2}}\right)\otimes \left(\widetilde{e^{1}}+3\widetilde{e^{2}}\right)\otimes (2\widetilde{e_{1}}-\widetilde{e_{2}})$+$$\widetilde{t_{jk}^{i}}=\left(\widetilde{e^{1}}+2\widetilde{e^{2}}\right)\otimes \left(\widetilde{e^{1}}+3\widetilde{e^{2}}\right)\otimes (3\widetilde{e_{1}}-2\widetilde{e_{2}}-\widetilde{e_{1}}+\widetilde{e_{2}})=\left(\widetilde{e^{1}}+2\widetilde{e^{2}}\right)\otimes \left(\widetilde{e^{1}}+3\widetilde{e^{2}}\right)\otimes (2\widetilde{e_{1}}-\widetilde{e_{2}})$$
  
-$\widetilde{t_{21}^{1}}=\left(\widetilde{e^{1}}+2\widetilde{e^{2}}\right)\otimes \left(\widetilde{e^{1}}+3\widetilde{e^{2}}\right)\otimes (2\widetilde{e_{1}}-\widetilde{e_{2}})\left(\widetilde{e_{2}},\widetilde{e_{1}},\widetilde{e^{1}}\right)=$+$$\widetilde{t_{21}^{1}}=\left(\widetilde{e^{1}}+2\widetilde{e^{2}}\right)\otimes \left(\widetilde{e^{1}}+3\widetilde{e^{2}}\right)\otimes (2\widetilde{e_{1}}-\widetilde{e_{2}})\left(\widetilde{e_{2}},\widetilde{e_{1}},\widetilde{e^{1}}\right)=$$
  
-$\left(\widetilde{e^{1}}\left(\widetilde{e_{2}}\right)+2\widetilde{e^{2}}\left(\widetilde{e_{2}}\right)\right)\otimes \left(\widetilde{e^{1}}\left(\widetilde{e_{1}}\right)+3\widetilde{e^{2}}\left(\widetilde{e_{1}}\right)\right)\otimes (2\widetilde{e_{1}}\left(\widetilde{e^{1}}\right)-\widetilde{e_{2}}\left(\widetilde{e^{1}}\right))=$+$$\left(\widetilde{e^{1}}\left(\widetilde{e_{2}}\right)+2\widetilde{e^{2}}\left(\widetilde{e_{2}}\right)\right)\otimes \left(\widetilde{e^{1}}\left(\widetilde{e_{1}}\right)+3\widetilde{e^{2}}\left(\widetilde{e_{1}}\right)\right)\otimes (2\widetilde{e_{1}}\left(\widetilde{e^{1}}\right)-\widetilde{e_{2}}\left(\widetilde{e^{1}}\right))=$$
  
-$\left(0+2\right)\otimes \left(1+3\cdot0\right)\otimes (2-0)=2\otimes 1\otimes 2=4$+$$\left(0+2\right)\otimes \left(1+3\cdot0\right)\otimes (2-0)=2\otimes 1\otimes 2=4$$
  
 ==== 47.13. ====  ==== 47.13. ====