矩阵迹的计算tr（AB)=tr(BA)

设A＝﹙aij﹚ B＝﹙bij﹚
tr﹙AB﹚＝∑[1≤i≤n]∑[1≤j≤n]aij×bji
tr﹙BA﹚＝∑[1≤i≤n]∑[1≤j≤n]bij×aji [把字母i,j对换]
＝∑[1≤j≤n]∑[1≤i≤n]bji×aij [bji×aij＝aij×bji]
＝∑[1≤j≤n]∑[1≤i≤n]aij×bji [改变∑次序.即n²个数的和,先按列加与先按行加是一样的]
＝∑[1≤i≤n]∑[1≤j≤n]aij×bji＝tr﹙AB﹚