class: center, middle, inverse, title-slide # Useful Formulas ## Linear Algebra ### Prof. Rozenn Dahyot ###
--- ## Differentiation w.r.t. vector Useful formula for vector `\(\mathbf{x}\)` , and a matrix `\(\mathrm{A}\)` : `$$\frac{\partial (\mathrm{A}\mathbf{x})}{\partial \mathbf{x}}=\mathrm{A}^{T}$$` `$$\frac{\partial (\mathbf{x}^{T}\mathrm{A})}{\partial \mathbf{x}}=\mathrm{A}$$` `$$\frac{\partial (\mathbf{x}^{T}\mathbf{x})}{\partial \mathbf{x}}=2 \mathbf{x}$$` `$$\frac{\partial (\mathbf{x}^{T}\mathrm{A}\mathbf{x})}{\partial \mathbf{x}}=\mathrm{A} \mathbf{x}+\mathrm{A}^{T} \mathbf{x}$$`