Transpose vs Inverse Matrix
Kev hloov pauv thiab qhov thim rov qab yog ob hom matrices nrog cov khoom tshwj xeeb peb ntsib hauv matrix algebra. Lawv sib txawv ntawm ib leeg, thiab tsis sib koom nrog kev sib raug zoo vim kev ua haujlwm kom tau txais lawv txawv.
Lawv muaj cov ntawv thov dav hauv thaj chaw ntawm cov kab zauv kab zauv thiab cov kev siv tau los xws li kev tshawb fawb hauv computer.
Ntau txog Transpose Matrix
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 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 cov lwm yam 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 yog sib npaug rau nws qhov tsis zoo ntawm transpose, lub matrix yog skew symmetric. Lub conjugate transpose ntawm ib tug matrix yog lub transpose ntawm lub matrix nrog lub ntsiab hloov nrog nws complex conjugate.
Ntau txog Inverse Matrix
Inverse of a matrix txhais tau tias yog matrix uas muab tus lej matrix thaum sib npaug ua ke. Yog li ntawd, los ntawm kev txhais, yog AB=BA=I ces B yog inverse matrix ntawm A thiab A yog inverse matrix ntawm B. Yog li, yog tias peb xav txog B=A -1, ces AA -1 =A -1 A=I
Rau lub matrix yuav invertible, qhov tsim nyog thiab txaus mob yog tias tus txiav txim ntawm A tsis yog xoom; i.e | A |=det(A) ≠ 0. Ib tug matrix yog hais tias yuav invertible, tsis yog lus, los yog tsis-degenerative yog hais tias nws txaus siab rau tus mob no. Nws ua raws li A yog ib qho square matrix thiab ob qho tib si A -1 thiab A muaj qhov loj tib yam.
Tus inverse ntawm matrix A tuaj yeem xam los ntawm ntau txoj hauv kev hauv kab zauv xws li Gaussian tshem tawm, Eigendecomposition, Cholesky decomposition, thiab Carmer txoj cai. Lub matrix kuj tseem tuaj yeem hloov pauv los ntawm txoj kev thaiv kev hloov pauv thiab Neuman series.
Dab tsi yog qhov txawv ntawm Transpose thiab Inverse Matrix?
• Transpose yog tau los ntawm rearranging cov kab thiab kab nyob rau hauv lub matrix thaum lub inverse yog tau los ntawm ib tug kuj nyuaj cov zauv xam. (Tab sis qhov tseeb ob leeg yog linear transformations)
• Raws li qhov tshwm sim ncaj qha, cov ntsiab lus hauv kev hloov pauv tsuas yog hloov lawv txoj haujlwm, tab sis cov txiaj ntsig zoo ib yam. Tab sis nyob rau hauv inverse, tus lej yuav txawv kiag li ntawm tus thawj matrix.
• Txhua lub matrix tuaj yeem muaj qhov hloov pauv, tab sis qhov hloov pauv tsuas yog txhais tau rau square matrices, thiab tus txiav txim siab yuav tsum yog tus txiav txim tsis yog xoom.
