# 正交

（重定向自正交函数

${\displaystyle \mathbf {A} ={\begin{bmatrix}1&2\\3&4\end{bmatrix}}}$

## 各种正交概念

### 正交变换

${\displaystyle \langle Tx,Ty\rangle =\langle x,y\rangle .}$

## 正交函数集

${\displaystyle \langle f,g\rangle _{w}=\int _{a}^{b}f(x)g(x)w(x)\,dx.}$

${\displaystyle \int _{a}^{b}f(x)g(x)w(x)\,dx=0.}$

${\displaystyle ||f||_{w}={\sqrt {\langle f,f\rangle _{w}}}}$

${\displaystyle \langle f_{i},f_{j}\rangle =\int _{-\infty }^{\infty }f_{i}(x)f_{j}(x)w(x)\,dx=||f_{i}||^{2}\delta _{i,j}=||f_{j}||^{2}\delta _{i,j}}$

${\displaystyle \delta _{i,j}={\begin{cases}1&\mathrm {if} \ i=j\\0&\mathrm {if} \ i\neq j\end{cases}}}$

${\displaystyle \langle f_{i},f_{j}\rangle =\int _{-\infty }^{\infty }f_{i}(x)f_{j}(x)w(x)\,dx=\delta _{i,j}}$

## 外部連結

1. ^ Lou, Chunbo; Ouyang, Qi; Guo, Xian; Hou, Junran; Ji, Xiangyu; Lyu, Cheng; Zhang, Haoqian M.; Zong, Yeqing. Insulated transcriptional elements enable precise design of genetic circuits. Nature Communications. 2017-07-03, 8 (1): 52. ISSN 2041-1723. doi:10.1038/s41467-017-00063-z （英语）.
2. ^ Naseri, Gita; Balazadeh, Salma; Machens, Fabian; Kamranfar, Iman; Messerschmidt, Katrin; Mueller-Roeber, Bernd. Plant-Derived Transcription Factors for Orthologous Regulation of Gene Expression in the Yeast Saccharomyces cerevisiae. ACS Synthetic Biology. 2017-09-15, 6 (9): 1742–1756. doi:10.1021/acssynbio.7b00094.
3. ^ Segall-Shapiro, Thomas H; Meyer, Adam J; Ellington, Andrew D; Sontag, Eduardo D; Voigt, Christopher A. A ‘resource allocator’ for transcription based on a highly fragmented T7 RNA polymerase. Molecular Systems Biology. 2014-07-30, 10 (7): 742. ISSN 1744-4292. PMC 4299498. PMID 25080493. doi:10.15252/msb.20145299.
4. ^ Green, Alexander A.; Silver, Pamela A.; Collins, James J.; Yin, Peng. Toehold Switches: De-Novo-Designed Regulators of Gene Expression. Cell. 2014-11-06, 159 (4): 925–939. ISSN 0092-8674. PMC 4265554. PMID 25417166. doi:10.1016/j.cell.2014.10.002.
5. ^ Roybal, Kole T.; Williams, Jasper Z.; Morsut, Leonardo; Rupp, Levi J.; Kolinko, Isabel; Choe, Joseph H.; Walker, Whitney J.; McNally, Krista A.; Lim, Wendell A. Engineering T cells with Customized Therapeutic Response Programs Using Synthetic Notch Receptors. Cell. 2016-10-06, 167 (2): 419–432.e16. ISSN 0092-8674. PMC 5072533. PMID 27693353. doi:10.1016/j.cell.2016.09.011.
6. ^ Elowitz, Michael B.; Kim, Matthew S.; Chong, Lucy S.; Gao, Xiaojing J. Programmable protein circuits in living cells. Science. 2018-09-21, 361 (6408): 1252–1258. ISSN 1095-9203. PMID 30237357. doi:10.1126/science.aat5062 （英语）.