矩阵的运算规则

加法
  
  (large A + B = B + A)
  
  (large (A + B) + C = A + (B + C))

与数相乘
  
  (large (λμ)A=λ(μA))
  
  (large (λ+μ)A =λA+μA)
  
　　(large λ (A+B)=λA+λB)

矩阵相乘
  
  (large (AB)C = A(BC))
  
  (large A(B pm C) =AB pm AC)
  
  (large (B pm C)A =BA pm CA)
  
  (large (λA)B = λ(AB) = A(λB))

转置
  记做 (large A^{T}) 或 (small A^{`})
  
  (large (A^{T})^{T} = A)
  
  (large (A+B)^{T} = A^{T} + B^{T})
  
  (large (AB)^{T} = B^{T}A^{T})
  
  (large (λA)^{T} = λA^{T})

导数
https://en.wikipedia.org/wiki/Matrix_calculus#Derivatives_with_vectors
  
  布局
    矩阵求导结果有两种写法
    分子布局
  
      (large frac{partial Y}{partial x}=egin{bmatrix}frac{partial y_{11}}{partial x} &...& frac{partial y_{1j}}{partial x} & ... & frac{partial y_{1m}}{partial x} \frac{partial y_{i1}}{partial x} &...& frac{partial y_{ij}}{partial x} & ... & frac{partial y_{im}}{partial x}\ frac{partial y_{n1}}{partial x} &...& frac{partial y_{nj}}{partial x}& ... &frac{partial y_{nm}}{partial x} end{bmatrix})
    
    分母布局
  
      (large frac{partial y}{partial X}=egin{bmatrix}frac{partial y}{partial x_{11}} &...& frac{partial y}{partial x_{1j}} & ... & frac{partial y}{partial x_{1m}} \frac{partial y}{partial x_{i1}} &...& frac{partial y}{partial x_{ij}} & ... & frac{partial y}{partial x_{im}}\ frac{partial y}{partial x_{n1}} &...& frac{partial y}{partial x_{nj}}& ... &frac{partial y}{partial x_{nm}}end{bmatrix})