self.assertEqual(rank_aaH, rank_aaH_hermitian) aHa = torch.matmul(a.mH, a) self.assertEqual(matrix_rank(aHa), matrix_rank(aHa, hermitian=True)) # check against NumPy self.assertEqual(rank_a, np.linalg.matrix_rank(a.cpu().numpy())) self.assertEqual(matrix_rank(a, 0.01), np.linalg...
AHA = AAH 2. unitarily diagonalizable 3. ∥Ax∥ = ∥AHx∥ 4. Ax = λx ⇔ AHx = x 5. if λ1 ≠λ2, x1⊥x2 eigenvector x x ? ? x P-1x Orthogonal 1. ATA = I = AAT 2. det(A) = ±1 3. λ = ±1 4. <Ax,Ay> = <x,y> (充要) 5. ∥Ax∥ = ∥x∥ (充...
A-1 1/λ x B~A λ P-1x Ⅱ Ⅱ② Ⅱ② Ⅱ① Ⅱ Ⅱ Skew-Symmetric AH=-Adet(A)=purerealorpureimagineλispureimagine Normal AHA=AAHunitarilydiagonalizable∥Ax∥=∥AHx∥Ax=λx⇔AHx=xifλ1≠λ2,x1⊥x2 Positivedefinite λ≥0det(A)≥0Δk(A)≥0 Unitary AHA=I=AAH|det(A)|=1|λ...
yS(aad)nikWaegyarsdatimeaghfreoaamrttfhs(oaoer)uftrhuceeelfsueewnleietrnhgeiyrngdytihdsetirsctirboiubnutfiitogionunraaanntdidoeennnoggfiinntehesespphe(ceebicaf)iivcfiayct-iadotniuodtnyatd(aHa. tDa.) diesel engine; and FFiigguurere1.2(ad)isWpalastyeshtehaet ssoyusrtceems wlaityhoinuttha...