Matrix Calculus

IngSM

Ukuthenga ngaphakathi nohlelo

Mayelana nalolu hlelo lokusebenza

I-Matrix Calculus iyisibali sohlelo lokusebenza esingcono kakhulu samanje sokusebenza kwezibalo okubandakanya izinombolo, omatikuletsheni kanye no-matrics we-multi-dimensional wezinombolo zangempela neziyinkimbinkimbi.
iyakwazi ukwenza zonke izibalo ezijwayelekile zezibalo ezinombolweni, ama-vector (omatrices kasayizi 1) kanye nomatikuletsheni ukusuka ku-2 kuya ku-5 dimensions.
Izinombolo zingaba ngokoqobo noma zibe yinkimbinkimbi, kokubili ekusebenzeni okujwayelekile kanye nakumatikuletsheni;
I-Matrix Calculus nayo inokhiye okuvumela ukuthi usebenze kuphela emkhakheni wangempela noma emkhakheni oyinkimbinkimbi,
ngaleyo ndlela unikeze iphutha uma insimu ingokoqobo futhi umphumela wokusebenza uyinkimbinkimbi;
ukusebenza ngezinombolo eziyinkimbinkimbi I-Matrix Calculus idinga inkokhelo yangaphakathi nohlelo.
Okuwukuphela kwemikhawulo ka-matrics yilena elandelayo:
- Ubukhulu be-matrix kusuka ku-1 kuye ku-5
- Ubude obuphelele be-matrix obungaphansi kuka-3200
- Ubude obukhulu be-matrix dimension = 50

Imisebenzi engenzeka yizinga lezibalo kanye nokusebenza kwe-matrix elandelayo:

* = i-matrix yomkhiqizo
/ = ukuhlukaniswa kukamatikuletsheni amabili, noma umkhiqizo we-matrix ephambene
^ = amandla e-matrix
+ = isamba sematrix
- = umehluko we-matrix
Det = Ukunquma
I-Tra = i-matrix transpose
I-Inv = i-matrix ephambene
I-Adj = i-matrix ehlangene
tr(A) = umkhondo we-matrix A
Iyunithi = iyunithi ye-matrix
Isikhundla = izinga le-matrix
I-Erf = isiza somsebenzi wephutha
REF = i-matrix ku-Row Echelon Form (isixazululo sohlelo)
Imisebenzi elandelayo ye-matrix isebenza kuphela ngenguqulo ye-Pro:
I-Inv+ = Moore - I-Penrose pseudo inverse
Eigen = ama-matrix eigenvalues
I-Evect = i-matrix eigenvectors
I-Vsing = amanani e-matrix ubunye S
I-Uvect = i-vector yesokunxele i-matrix eyodwa U
I-Vvect = i-vector eyodwa ye-matrix V
I-Dsum = isamba esiqondile se-matrix
Ongaphandle = umkhiqizo wangaphandle
L(L*L’) = I-matrix engunxantathu ephansi L ukuze A = L*L’
Q(Q*R) = I-matrix yesokunxele ukuze A = Q*R
R(Q*R) = Wright matrix R kuze kube ngu-A = Q*R
Jordan = Jordan matrix J
||A|| = Frobenius evamile
e^A = i-exponential ye-matrix A
√ A = impande yesikwele matrix

Uma i-matrix ivumela, kuyenzeka futhi ukubala umsebenzi we-matrix, lapho umsebenzi ungomunye waleyo yesibali, isibonelo (A = matrix):
lne (A), log (A), sin (A) cos (A), tan (A), sinh (A), arcsin (A), arctanh (A)