# Tag Info

### Why is the derivative of the real absolute squared different to complex absolute squared

\begin{align} \frac{\partial }{\partial x} |z|^2 &= \frac{\partial}{\partial x} (x^2 + y^2)\\ &= 2x \end{align} No contradiction. The derivative of $|z|^2$ with respect to $x$ along the ...
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### Prove that the following is incompressible (ie divergence is zero)

I am guessing that the quantity $Q= \vec r\cdot S \cdot\vec r$ is a scalar-valued expression, a quadratic function constructed from a symmetric matrix $S$ that has constant coefficients and no trace. ...
• 2,073
Accepted

• 127k
1 vote

### Inner product is invariant under reflections in the real hyperplane?

$r_v(u) = 2d(u,v)v-u$, $$d(r_v(u),r_v(w)) = d(2d(u,v)v-u,2d(w,v)v-w)$$ $$= -1 \times d(u,2d(w,v)v-w) + 2d(u,v) \times d(v,2d(w,v)v-w)$$  = -1 \times (2d(u,v)\times d(w,v) - d(u,w)) + 2d(u,v) \...
• 1,254
1 vote
Accepted

### What is the operation that happens between a tensor product and a vector under matrix multiplication?

I would recommend Schuller's lecture on Multilinear Algebra for a very nice from-the-ground-up description of vector spaces and tensors, but it doesn't include a discussion of the tensor product. Lee'...
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