Yog li ntawd, muab cov lej A = (theij)mxn qhov hloov pauv ntawm A yog At = (a 'ji) nxm.

 

i: txoj haujlwm rau ntawm txoj kab
j: kem txoj haujlwm
unij: ib qho array keeb ntawm txoj hauj lwm ij
m: tus naj npawb ntawm cov kab hauv matrix
n: cov naj npawb ntawm hauv cov lej
Unt: transpose kev nqus ntawm A

Nco ntsoov tias matrix A yog kev txiav txim mxn, thaum nws transpose At yog ntawm kev txiav txim nx m.

Piv txwv

Nrhiav qhov transpose kev ua lej ntawm matrix B.

Raws li qhov muab los qhia yog ntawm hom 3 × 2 (3 kab thiab 2 kab), nws txoj kev hloov pauv yuav yog hom 2 × 3 (2 kab thiab 3 kab).
Txhawm rau tsim qhov kev hloov pauv sib npaug, peb yuav tsum sau tag nrho cov kab ntawm B ua kab ntawm BtCov. Raws li qhia hauv daim duab hauv qab no:

Yog li, transpose matrix ntawm B yuav yog:

kuj pom thiab: Arrays

Cov cuab yeej ntawm transpose matrix

  • (At)t = A: qhov khoom ntiag tug no qhia tau hais tias kev sib hloov ntawm qhov sib pauv hloov sib npaug yog thawj qhov sib npaug.
  • (A + B)t = At + B.t: Qhov kev hloov pauv ntawm cov lej ntawm ob qhov kev sib tw yog sib npaug ntawm cov lej ntawm kev sib hloov ntawm lawv.
  • (A. IB)t = IBt . Unt: Kev hloov pauv ntawm cov sib npaug ntawm ob qho kev sib tw yog sib npaug ntawm cov khoom ntawm qhov hloov ntawm lawv, hauv kev txiav txim rov qab.
  • det (M) = det (Mt): Qhov txiav txim siab ntawm qhov sib hloov ntawm qhov sib npaug yog tib yam li kev txiav txim siab ntawm qhov qub.

Symmetric matrix

Ib qhov ntsuas (matrix) hu ua symmetric thaum, rau qee yam ntawm matrix A, qhov sib luag aij = aji Nws yog qhov tseeb tiag

Matrices ntawm hom no yog cov square matrices, uas yog, tus naj npawb ntawm cov kab yog sib npaug ntawm cov lej.

Txhua kab zauv hauv qab no ua raws cov kev sib raug zoo hauv qab no:

A = Uat

Yam txawv hauv qab ntuj

Nws yog ib qho tseem ceeb kom tsis txhob cuam tshuam qhov sib npaug ntawm qhov sib txawv nrog transpose ib. Qhov ntsuas rov qab yog ib qho uas muaj tib lub ntsiab hauv kab thiab kab, txawm li cas los xij, muaj cov paib sib txawv. Yog li ntawd, cov lus rov los ntawm B yog –B.

Rov qab ntsuas qhov tseeb

Lub inverse matrix (qhia los ntawm tus lej –1) yog ib qho uas cov khoom ntawm ob qho kev sib npaug yog sib npaug ntawm cov duab plaub xwm txheej ntawm square matrix (I) ntawm tib qho kev txiav txim.

Piv txwv:

A. B = B. A = Kuvn (thaum matrix B tsis rov qab txog ntawm Matrix A)

hloov pauv

Vestibular ce nrog cov tswv yim

1Cov. (Fei-SP) Muab rau hauv Matrix A =, qhov twg At nws txoj kev sib hloov, kev txiav txim siab ntawm matrix A. At Es:

a) 1
b) 7
c) 14
d) 49

2Cov. (FGV-SP) A thiab B yog lub hauv paus thiab At yog qhov kev ntsuas sib hloov ntawm A. Yog tias, tom qab ntawv txhoj At Cov. B yuav thov rau:

a) x + y = -3
b) xwm. y = 2 hli
c) x/y = –4
d) x. thiab2 = -1
e) x/y = –8

3Cov. (UFSM-RS) Kev paub txog cov lej

sib npaug transpose, tus nqi ntawm 2x + y yog:

a) – 23 Nws
b) –11 ib
c) -1
d) 11
e) 23 hli