Chapter 57: matrix calculus
https://www.youtube.com/playlist?list=PLhcN-s3_Z7-YS6ltpJhjwqvHO1TYDbiZv
x=⟨x1,x2,⋯,xn⟩=[x1x2⋯xn]⊺=[x1x2⋮xn]
f(x1,x2,⋯,xn)=f(⟨x1,x2,⋯,xn⟩)=f(x) y=⟨y1,y2,⋯,ym⟩=[y1y2⋯ym]⊺=[y1y2⋮ym]
57.2 scalar-by-vector
∇f=∂∂xf=∂f∂x=⟨∂f∂x1,∂f∂x2,⋯,∂f∂xn⟩=[∂f∂x1∂f∂x2⋯∂f∂xn]⊺=[∂f∂x1∂f∂x2⋮∂f∂xn]
fi=fi(x1,x2,⋯,xn)=fi(x)
f=⟨f1,f2,⋯,fm⟩=[f1f2⋯fm]⊺=[f1f2⋮fm]
57.3 vector-by-vector
57.3.1 numerator-layout notation
分子布局
∂y∂x=[∂y1∂x∂y2∂x⋮∂yp∂x]=[∂y∂x1∂y∂x2⋯∂y∂xn]=[∂y1∂x1∂y1∂x2⋯∂y1∂xn∂y2∂x1∂y2∂x2⋯∂y2∂xn⋮⋮⋱⋮∂ym∂x1∂ym∂x2⋯∂ym∂xn]=[∂yi∂xj]m×n
references
14.
ccjou. 矩陣導數. (2013).