N × n Fourier matrix yog ib qho nyuaj Hadamard matrix nrog rau (j, k) nkag (1 / n) e (2 i π / n) j k rau j, k=1, 2, …, n. Ib tug tuaj yeem qhia tau tias nws yog unitary thiab tsis muaj xoom nkag.
Koj paub li cas yog matrix yog unitary?
Ib tug matrix yog a matrix uas nws inverses nws conjugate transpose. Unitary matrices yog cov complex analogue ntawm tiag tiag orthogonal matrices. Yog tias U yog square, complex matrix, ces cov xwm txheej hauv qab no yog sib npaug: U yog unitary.
Puas yog ib lub matrix ua tau tiag?
Yog tias tag nrho cov kev nkag ntawm ib lub matrix yog tiag tiag (piv txwv li, lawv qhov nyuaj yog tag nrho xoom), ces tus matrix tau hais tias yog orthogonal. Txij li thaum lub orthogonal matrix yog unitary, tag nrho cov khoom ntawm unitary matrices siv rau orthogonal matrices.
Puas yog txhua tus matrix ib txwm muaj?
A ib txwm matrix yog unitary yog thiab tsuas yog tias tag nrho nws cov eigenvalues (nws spectrum) pw ntawm chav tsev voj voog ntawm lub dav hlau complex. Hauv lwm lo lus: Ib txwm matrix yog Hermitian yog thiab tsuas yog tias tag nrho nws cov eigenvalues yog tiag. Feem ntau, cov sum los yog cov khoom ntawm ob ib txwm matrices yuav tsum tsis yog ib txwm.
Puas yog unitary matrices nws tus kheej adjoint?
Kev ceeb toom tias ob tus kheej adjoint matrices thiab unitary matrices yog qhov qub thiab yog li lawv yog orthogonally diagonalizable.
