Chapter 57: matrix calculus

14

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x=x1,x2,,xn=[x1x2xn]=[x1x2xn]

f(x1,x2,,xn)=f(x1,x2,,xn)=f(x) y=y1,y2,,ym=[y1y2ym]=[y1y2ym]

57.1 vector-by-scalar

yx=[y1xy2xymx]

57.2 scalar-by-vector

f=xf=fx=fx1,fx2,,fxn=[fx1fx2fxn]=[fx1fx2fxn]

fi=fi(x1,x2,,xn)=fi(x)

f=f1,f2,,fm=[f1f2fm]=[f1f2fm]

57.3 vector-by-vector

57.3.1 numerator-layout notation

分子布局

yx=[y1xy2xypx]=[yx1yx2yxn]=[y1x1y1x2y1xny2x1y2x2y2xnymx1ymx2ymxn]=[yixj]m×n

57.3.2 denominator-layout notation

分母布局

yx=[yx1yx2yxn]=[y1xy2xymx]=[y1x1y2x1ymx1y1x2y2x2ymx2y1xny2xnymxn]=[yjxi]n×m

https://zhuanlan.zhihu.com/p/692195114

references

14.
ccjou. 矩陣導數. (2013).