Nyob rau hauv vector calculus, Jacobian matrix ntawm vector-valued muaj nuj nqi ntawm ntau qhov sib txawv yog cov matrix ntawm tag nrho nws cov thawj-qib ib feem derivatives.
Jacobian matrix yog dab tsi?
Jacobian matrix sawv cev qhov sib txawv ntawm f ntawm txhua qhov chaw uas f yog qhov sib txawv … (y – x) yog qhov zoo tshaj linear approximation ntawm f(y) rau tag nrho cov ntsiab lus y ze rau x. Qhov kev ua haujlwm no yog hu ua derivative lossis qhov sib txawv ntawm f ntawm x.
Yakhauj ntsuas dab tsi?
Tus nqi tiag tiag ntawm Jacobian ntawm kev sib koom ua ke kev hloov pauv kuj tseem siv los hloov ntau qhov sib xws los ntawm ib qho system mus rau lwm qhov. Hauv R2 nws ntsuas ntau npaum li cas chav tsev yog distorted los ntawm qhov muab hloov pauv, thiab hauv R3 qhov ntsuas no ntsuas qhov unit ntim distortion, thiab lwm yam.
Puas yog Jacobian matrix ib txwm yog square matrix?
The jacobian matrix tuaj yeem yog txhua daim ntawv. Tej zaum nws yuav yog square matrix (tus naj npawb ntawm kab thiab kab sib npaug) los yog cov duab plaub (cov kab thiab kab tsis sib npaug).
Puas yog Jacobian matrices Square?
Ib Jacobian Matrix tuaj yeem txhais tau tias yog matrix uas muaj thawj qhov kev txiav txim ib nrab rau kev ua haujlwm vector. Jacobian Matrix tuaj yeem ua tau ntawm txhua daim ntawv. Nws tuaj yeem yog cov duab plaub, qhov twg cov kab thiab kab tsis zoo ib yam, lossis nws tuaj yeem yog square matrix, qhov twg cov kab thiab kab sib npaug.
