2.3 奇异值分解
奇异值的分解在某些方面与对称矩阵或者Hermite矩阵基于特征向量的对角化类似
如:
>> A = rand(5) A = 664/815 694/7115 589/3737 689/4856 3581/5461 1298/1433 408/1465 6271/6461 407/965 489/13693 751/5914 1324/2421 581/607 1065/1163 439/517 717/785 338/353 614/1265 61/77 283/303 1493/2361 687/712 1142/1427 1966/2049 1481/2182 >> [V,D,U] = svd(A) V = -1749/7066 -2221/3966 937/2268 129/224 561/1601 -611/1725 -4813/9244 -2543/3356 -131/11843 -1058/6197 -536/1155 721/1199 -413/2460 1375/2268 -229/1386 -1313/2398 -496/4191 494/1039 -1015/3063 -525/887 -457/837 154/773 -139/4660 -308/705 1011/1474 D = 1567/473 0 0 0 0 0 1210/1283 0 0 0 0 0 1629/1949 0 0 0 0 0 2585/5344 0 0 0 0 0 79/3990 U = -379/880 -1401/1585 337/6355 -479/5417 1291/8591 -752/1745 740/3353 1205/6144 -175/239 -274/627 -1919/4156 184/2067 -516/691 847/2734 -527/1489 -307/649 937/2532 -95/1191 -639/6247 815/1033 -2200/5023 1510/9527 551/877 1124/1901 -572/2907 >> help svd svd - 奇异值分解 此 MATLAB 函数 以降序顺序返回矩阵 A 的奇异值。 s = svd(A) [U,S,V] = svd(A) [U,S,V] = svd(A,'econ') [U,S,V] = svd(A,0)