Here (1) opposed to here (2) concern similar ideas about derivatives. $(1)$ appears to discuss integer ordered derivatives and possibly anti-derivatives, while $(2)$ is more concerned with the fractional derivatives. $(2)$ has a neat tag designed just for it, called [fractional-calculus]. Howe...
$$Q= \begin{bmatrix} \cos x & -\sin x\\ \sin x & \cos x\end{bmatrix}$$ Given x belongs to $\mathbb{R^2}$, show $Qx$ and $x$ are equidistant. I've tried dot producting $Qx$ and seeing whether they are equal. I just can't seem to get it.
I'm trying to understand the cosine similarity in a simple and graphical way, very much similar to this question here but I do not understand how the person got to their answer.
We know that regular hexagons can tile the plane but not in a self-similar fashion. However we can construct a fractal known as a Gosper island, that has the same area as the hexagon but has the property that when surrounded by 6 identical copies produces a similar shape, but with dimensions scal...
Let be $$A=\begin{pmatrix} \frac{-3}{2} & 2 & \frac{-1}{2} \\ \frac{-1}{2} & 0 & \frac{1}{2} \\ \frac{1}{2} & -2 & \frac{3}{2} \end{pmatrix}, B=\begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{pmatrix}$$ Prove that A and B are similar. I know if we can find a matrix $P$ so that $A=P^{-1}...
I'm trying to calculate the vertex cosine similarity of a weighted directional graph, however struggling to understand the concept. While I understand the methodology for simple and directed graphs, weighted has me stumped. I'm following the examples provided by wolfram here however with the wei...
Consider two 3D polylines, A and B. I am interested in computing a distance/similarity between them (from their current positions, no need to find the "best overlap" first). I have come up with some reasonable approximations (average distance between all points on A to their closest points on B, ...
The given task is to find all 2x2 Matrices A that are similar to: a) $\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$ b) $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ c) $\begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}$ However, I don't really know which steps to t...
Let $M_n(K)$ be the set of all $n\times n$ matrices over a field $K$. If $\mathcal{R}$ is the equivalence relation defined by matrix similarity, what does the quotient $M_n(K)/\mathcal{R}$ looks like? Is there something that characterizes it in terms of cardinality? Is there a way to extend matri...
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