&&\parallel\sigma(t,x)^{-1}b(t,x)\parallel^2\\ &=&b(t,x)^{\top}(\sigma(t,x)\sigma(t,x)^{\top})^{-1}b(t,x)\\ &=&\sum_{i=1}^n\sum_{j=1}^nc_i(t,x)c_j(t,x)a_i(t,x)(\sigma(t,x)\sigma(t,x)^{\top})^{-1}a_j(t,x)\\ &=&\sum_{i=1}^n\sum_{j=1}^n\frac{c_i(t,x)c_j(t,x)}{\lambda_j(t,x)}a_i(t,x)a_j(t,x)\\ &=&\sum_{i=1}^n\frac{c_i(t,x)^2}{\lambda_i(t,x)}\quad (\{a_i(t,x)\}:{\rm orthonormal\ basis})\\ &\leq &\frac{1}{\lambda}\parallel b(t,x)\parallel^2\\ &\leq &M\quad (M:{\rm const},\quad b(t,x):{\rm uniformly\ bounded})
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  1. http://formula.s21g.com/?%26%26%5Cparallel%5Csigma(t,x)%5...
  2. https://mkprob.hatenablog.com/entry/20121101/1351746957
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  4. http://mkprob.hatenablog.com/entry/20130220/1361363246
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