Describe the mistake
Equation 5.147 contains a small typo. This is the very first time Hessian is defined in this book, so I believe it’s more natural to use its original form, where $H[2, 1]=\frac{\partial^{2}f}{\partial y\partial x}$, instead of $H[2, 1]=\frac{\partial^{2}f}{\partial x\partial y}$.
I understand maybe the authors are merely making it clearer that Hessian matrix is symmetric for twice continuously differentiable functions, but using the original Hessian definition wouldn’t make it any harder to figure it out since $\frac{\partial^{2}f}{\partial x\partial y}=\frac{\partial^{2}f}{\partial y\partial x}$ is pointed out in equation 5.146, just a few lines above.
Location
Version: Draft 2021-07-29
Chapter 5.7
Page 165
Equation number 5.147
Proposed solution
Change Hessian definition from $H[2, 1]=\frac{\partial^{2}f}{\partial x\partial y}$ to $H[2, 1]=\frac{\partial^{2}f}{\partial y\partial x}$.
Describe the mistake Equation 5.147 contains a small typo. This is the very first time Hessian is defined in this book, so I believe it’s more natural to use its original form, where $H[2, 1]=\frac{\partial^{2}f}{\partial y\partial x}$, instead of $H[2, 1]=\frac{\partial^{2}f}{\partial x\partial y}$.
I understand maybe the authors are merely making it clearer that Hessian matrix is symmetric for twice continuously differentiable functions, but using the original Hessian definition wouldn’t make it any harder to figure it out since $\frac{\partial^{2}f}{\partial x\partial y}=\frac{\partial^{2}f}{\partial y\partial x}$ is pointed out in equation 5.146, just a few lines above.
Location
Proposed solution Change Hessian definition from $H[2, 1]=\frac{\partial^{2}f}{\partial x\partial y}$ to $H[2, 1]=\frac{\partial^{2}f}{\partial y\partial x}$.
Additional context None