Qhov txawv ntawm Transpose thiab Conjugate Transpose

2024 Tus sau: Alex Aldridge | [email protected]. Kawg hloov kho: 2023-12-17 13:40

Transpose vs Conjugate Transpose

Kev xa tawm ntawm matrix A tuaj yeem txheeb xyuas tau raws li cov matrix tau los ntawm kev hloov cov kab ua kab lossis kab ua kab. Raws li qhov tshwm sim, txhua qhov ntsuas qhov ntsuas tau hloov pauv. Ntau txoj cai, hloov pauv ntawm matrix A, txhais tau tias yog

qhov twg

Nyob rau hauv ib tug transpose matrix, kab pheeb ces kaum tseem tsis hloov. Tab sis tag nrho lwm cov ntsiab lus yog tig ib ncig ntawm kab pheeb ces kaum. Tsis tas li ntawd, qhov loj ntawm cov matrices kuj hloov ntawm m × n mus rau n × m.

Cov transpose muaj qee yam khoom tseem ceeb, thiab lawv tso cai rau kev tswj hwm ntawm matrices yooj yim dua. Tsis tas li ntawd, qee qhov tseem ceeb transpose matrices raug txhais raws li lawv cov yam ntxwv. Yog hais tias lub matrix yog sib npaug rau nws transpose, ces lub matrix yog symmetrical. Yog hais tias lub matrix sib npaug rau nws qhov tsis zoo ntawm transpose, ces lub matrix yog skew symmetric.

Lub conjugate transpose ntawm lub matrix yog qhov hloov pauv ntawm matrix nrog cov ntsiab lus hloov nrog nws txoj kev sib txuas. Ntawd yog, lub complex conjugate (A^{) txhais tau tias yog kev hloov pauv ntawm txoj kev sib txuas ntawm matrix A.}

A=(Ā)^{T; Hauv kev nthuav dav,}

qhov twg

and ā_{ji ε C.}

Nws tseem hu ua Hermitian transpose thiab Hermitian conjugate. Yog hais tias lub conjugate transpose yog sib npaug rau lub matrix nws tus kheej, lub matrix yog hu ua Hermitian matrix. Yog hais tias conjugate transpose yog sib npaug rau qhov tsis zoo ntawm lub matrix, nws yog skew Hermitian matrix. Thiab yog hais tias tus inverse ntawm lub matrix yog sib npaug rau lub complex conjugate, lub matrix yog unitary.

Ib yam li ntawd, txhua qhov tshwj xeeb matrices complex conjugate kuj muaj cov khoom tshwj xeeb uas tuaj yeem siv los ua lej tswj tau yooj yim. Lub conjugate transpose yog dav siv nyob rau hauv quantum mechanics thiab nws cov hauj lwm.

Qhov txawv ntawm Transpose thiab Conjugate Transpose yog dab tsi?

• Transpose ntawm matrix yog tau los ntawm rearranging kab rau hauv kab, los yog kab rau hauv kab. Lub complex conjugate ntawm ib tug matrix yog tau los ntawm kev hloov txhua lub caij los ntawm nws cov complex conjugate (i.e x + iy ⇛ x-iy los yog vice versa). Lub conjugate transpose yog tau los ntawm kev ua ob qho haujlwm ntawm matrix.

• Yog li ntawd, conjugate transpose tsuas yog transpose matrix nrog nws txoj kev sib txuas ua ke.