Transcription of Matrix Calculus - Stanford University
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Matrix Calculus - Stanford University
Appendix DMatrix CalculusFrom too much study, and from extreme passion, cometh madnesse. Isaac Newton[205, 5] Gradient, Directional derivative, Taylor GradientsGradientof a differentiable real functionf(x) :RK Rwith respect to its vectorargument is defined uniquely in terms of partial derivatives f(x), f(x) x1 f(x) f(x) xK RK(2053)while the second-order gradient of the twice differentiable real function with respect toitsvector argument is traditionally called theHessian; 2f(x), 2f(x) x21 2f(x) x1 x2 2f(x) x1 xK 2f(x) x2 x1 2f(x) x22 2f(x) x2 2f(x) xK x1 2f(x) xK x2 2f(x) x2K SK(2054)interpreted 2f(x) x1 x2= f(x) x1 x2= f(x) x2 x1= 2f(x) x2 x1(2055)Dattorro,Convex Optimization Euclidean Distance Geometry,M oo, 2005, D.
to the Kronecker product of matrices ⊗ ; a.k.a, tensor product (kron() in Matlab). Although its definition sees reversal in the literature, [434, 2.1] Kronecker product is not
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