12:52 AM
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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...

7 hours later…
8:21 AM
The tag was created recently. Probably here:
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Let $A$ be an $n \times n$ matrix such that $AA^T \geq x^2I, x\geq 0$, which means that the matrix $AA^T-x^2I$ is positive semidefinite. Can we show that $(A+A^T)/2 \geq xI$? Thanks

Keep? Remove? Are there previous discussions about such tag?
(I found it when I saw question about symmetric matrices and I checked whether we have a separate tag for such matrices. I have added it to one question - maybe this increases probability that if somebody has objections to this tag, they will mention them somewhere.)

2 hours later…
10:13 AM
Another tags related to matrices, which was created recently, is .
There are two questions in that tag at the moment:
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$$Q= \begin{bmatrix} \cos x & -\sin x\\ \sin x & \cos x\end{bmatrix}$$ 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.

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Prove that if $A^t = A^{-1}$ then different rows of $A$ are orthogonal to each other I saw this statement in my linear algebra book and I don't really know how to prove it, I hope someone can help me out. Thank you in advance.

10:36 AM
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The tag similarity was created last month. It has empty tag info. Just by the name, there are two common uses of the word similarity in mathematics, namely similarity of matrices and similarity of geometrical objects. Using a word with several meanings as a name of a tag often leads to inconsis...

The tag looks like it could be problematic, because there are (at least) two possible meanings.
I have retagged this question a moment ago, it is about cosine similarity:
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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.

Questions currently in this tag are:
15

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...

1

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 $A=P^{-1}... 1 I'm trying to calculate the vertex cosine similarity of a weighted directional graph, however struggling to understand the concept. While I understand the methodology for simple and directed graphs, weighted has me stumped. I'm following the examples provided by wolfram here however with the wei... 0 Consider two 3D polylines, A and B. I am interested in computing a distance/similarity between them (from their current positions, no need to find the "best overlap" first). I have come up with some reasonable approximations (average distance between all points on A to their closest points on B, ... 0 The given task is to find all 2x2 Matrices A that are similar to: a)$\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}$However, I don't really know which steps to t... 3 Let$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}$looks like? Is there something that characterizes it in terms of cardinality? Is there a way to extend matri... 1 This seems like such a simple question, but I can't quite see a connection. I want to say that the two diagonal matrices can commute with each other, and this gives us the algebraic edge to show their similarity, but I'm generally bad with abstract algebra proofs. 2 hours later… 12:30 PM The tag also exists. The tag-excerpt was created by the same user. 2 hours later… 2:28 PM I see that the synonym$\to\$ has been suggested. It probably makes sense, since is already a synonym.