a = [0.7649 -1.1307 0.4523 -0.4518 1.3647 0.3554 -0.5567 1.0098 0.2519 -0.9025] b = [-0.9463 0.4038 -0.1295 0.2800 -0.4398 -0.0494 -0.2356 -0.2689 -1.5379 1.6788] dot(a,b) = -4.0261 c = [0.7219+0.8871i 0.7073-0.7953i 0.2610+0.4325i -0.0565-0.0719i 0.7277-0.9754i -0.3780+1.0718i] d = [-0.0821+0.8410i -0.0749+0.0729i -0.6094-0.2975i 0.2106-0.2026i 0.1043-0.8300i 0.0806+0.3698i] dot(c,d) = 0.3698+0.0806i a = [-0.5567 -0.1660 0.4452 0.3616] b = [-0.7418 0.4853 0.2524 0.9959 -0.0862 -0.4018 0.9459] outer_product(a,b) = [[0.4129 -0.2702 -0.1405 -0.5544 0.0480 0.2237 -0.5266] [0.1231 -0.0806 -0.0419 -0.1653 0.0143 0.0667 -0.1570] [-0.3302 0.2160 0.1124 0.4433 -0.0384 -0.1788 0.4211] [-0.2682 0.1755 0.0913 0.3601 -0.0312 -0.1453 0.3420]] c = [-0.1082+0.1311i 0.7747-0.3968i 0.1098+0.7432i -0.4435-1.1627i] d = [0.9996-0.7256i 0.0559+0.2146i -0.1613+0.5573i -0.6673-0.8023i 0.7836-0.8702i 1.1201+0.0713i -0.1312+1.2300i] outer_product(c,d) = [[-0.0130+0.2096i -0.0342-0.0159i -0.0556-0.0815i 0.1774-0.0007i 0.0293+0.1969i -0.1306+0.1392i -0.1471-0.1503i] [0.4865-0.9588i 0.1285+0.1441i 0.0962+0.4958i -0.8353-0.3568i 0.2619-0.9851i 0.8961-0.3892i 0.3864+1.0050i] [0.6491+0.6632i -0.1533+0.0651i -0.4319-0.0587i 0.5230-0.5840i 0.7328+0.4868i 0.0700+0.8403i -0.9286+0.0376i] [-1.2869-0.8404i 0.2247-0.1602i 0.7195-0.0596i -0.6369+1.1316i -1.3592-0.5252i -0.4138-1.3339i 1.4882-0.3929i]] outer_product(c,d,true) = [[-0.2033+0.0526i 0.0221+0.0306i 0.0905+0.0392i -0.0330-0.1743i -0.1989+0.0086i -0.1119+0.1546i 0.1755+0.1159i] [1.0623+0.1655i -0.0418-0.1884i -0.3461-0.3678i -0.1986+0.8863i 0.9523+0.3632i 0.8395-0.4997i -0.5897-0.9009i] [-0.4295+0.8226i 0.1656+0.0180i 0.3965-0.1811i -0.6696-0.4078i -0.5607+0.6780i 0.1760+0.8246i 0.8997-0.2326i] [0.4004-1.4840i -0.2743+0.0302i -0.5765+0.4347i 1.2287+0.4200i 0.6642-1.2970i -0.5796-1.2707i -1.3719+0.6980i]] M = [[1.5372 -0.2056 1.4815 -0.2982 0.2718] [0.4388 -0.0438 0.9243 -0.0744 -0.2958] [0.9199 -0.6124 1.2957 -0.1326 0.5585]] N = [[0.2996 -0.7612] [-1.2992 0.7938] [-0.8841 -1.0607] [-1.3342 0.3100] [0.6073 -0.2003]] M *= N; M = [[-0.0193 -3.0517] [-0.7090 -1.3130] [0.4417 -2.7137]] M = [[0.1005+1.0560i 0.1761-0.2764i 0.0458-1.0105i -0.1478-0.2132i] [0.1265-0.3484i 1.0178-0.5611i 0.8302-1.2998i -0.1693-0.4322i] [-0.2209+0.1667i -0.2342+0.5487i -0.2487-0.6300i -0.2915+0.7803i] [-0.5408+0.4760i 0.3200+0.7143i -0.1837+1.0963i -0.6752-0.0387i]] N = [[-0.7615+1.6166i 1.2962-0.1030i] [-0.2941-0.7994i -0.0933+0.2843i] [0.2678-1.0849i -0.8061+0.6237i] [0.2044+0.9265i -0.8699-0.7039i]] M *= N; M = [[-2.9731-1.2019i 0.8729+2.5670i] [-1.1029-1.6727i 0.1770+1.9378i] [-1.1265-0.4677i 0.9929+0.0002i] [1.1572-1.8433i -0.8604+0.2077i]] M = [[0.9967 1.6791 0.0965 -0.5851] [0.1380 1.2015 -1.4074 -0.2497] [-0.8319 -1.2126 -0.9693 1.7956]] v = [0.6205 -0.3411 0.0005 -1.9212] out = M * v = [1.1699 0.1548 -3.5528] M = [[-0.0060-0.2397i -1.6359+0.7692i] [0.0146+0.6869i 0.7382-0.5274i] [-0.7774-0.5661i -1.1268-0.6975i]] v = [1.2607-1.1375i -0.0444-0.4806i] out = M * v = [0.1622+0.4568i 0.5135+0.5180i -1.9091+0.7432i]