Rappels utiles Useful reminders (1)

• Produit scalaireDot product
  • wikipedia: Dot product
  • \(\mathbf {a} \cdot \mathbf {b} =\sum _{i=1}^{n}a_{i}b_{i}=a_{1}b_{1}+a_{2}b_{2}+\cdots +a_{n}b_{n}\)
• Vecteur transposéTransposed vector
  • wikipedia: Transpose
  • \(\left[\mathbf {A} ^{\operatorname {T} }\right]_{ij}=\left[\mathbf {A} \right]_{ji}\)
• Norme EuclidienneEuclidean norm
  • wikipedia: Euclidean norm
  • \(\|{\vec {u}}\|={\sqrt {x^{2}+y^{2}}}\)
• Produit MatricielMatrix product
  • wikipedia: Matrix multiplication
  • \(\mathbf {C} =\mathbf {A} \mathbf {B} \Leftrightarrow c_{ij}=\sum _{k=1}^{n}a_{ik}b_{kj}\)
  • \(\mathbf {A} \mathbf {I} =\mathbf {A} =\mathbf {I} \mathbf {A}\)

Rappels utiles Useful reminders (2)

• Dérivée partiellePartial derivative
  • wikipedia: Partial derivative
  • \(\frac{\partial f}{\partial x} = \lim_{h \to 0} \frac{f(x+h,y)-f(x,y)}{h}\)
• GradientGradient
  • wikipedia: Gradient
  • \(\nabla f = \left( \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y} \right)\)
• Dérivée en chaîneChain rule
  • wikipedia: Chain rule
  • \(h'=(f\circ g)'=(f'\circ g)\cdot g'\)
  • \(\frac {dz}{dx}={\frac {dz}{dy}}\cdot {\frac {dy}{dx}}\)

Fin de la partie 1End of part 1