# Questions tagged [proof-explanation]

This tag is for readers who ask for explanation and clarification of some steps of a particular proof.

5,360 questions
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### Proof of the proposition which says that the column rank of $A$ is equal to the row rank of $A$. (Gilbert Strang's new lecture)

I am watching this new lecture by Gilbert Strang. I have the following question. Let $A = \begin{bmatrix}2&1&3\\3&1&4\\5&7&12\\\end{bmatrix}$. Prof. Strang showed that ...
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### understanding this proof of the Cramer-Rao bound holding with equality

I've been looking at the following passage of Statistical Signal Processing (1991) by Louis Scharf. It deals with showing when the Cramer-Rao bound holds with equality. In this passage, $\mathbf{C}$ ...
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### Proving $2\cosh 2x+ \sinh x = 5$

I have been sitting on this question for quite some time and I haven't been able to prove this identity. Please anybody who can help me here. I am new to hyperbolics. $$2\cosh 2x+ \sinh x = 5$$ I ...
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### $\mathbb{R}\times\mathbb{R}$ $\cong$ $\mathbb{R}^2$ [duplicate]

In my topology class we proved that $\mathbb{R}\times\mathbb{R}$ $\cong$ $\mathbb{R}^2$, when $\mathbb{R}$ and $\mathbb{R}^2$ has the metric topology and $\mathbb{R}\times\mathbb{R}$ has the standard ...
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### Relationship between tangents and double roots

I am dealing with the proof of the following Theorem, taken from Dale Husemöller's book Elliptic Curves: I have trouble to understand the following underlined section of the proof: Could you please ...
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### Question on proof: cosets of the alternating group $A_n$

The theorem: If $n \ge 2$, then $|A_n| = \frac{n!}2$. Proof: We will proof that $S_n\backslash A_n$ is the only non-trivial coset of $A_n$ (so aside from $A_n$ itself). Consider an arbitrary, ...
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### Intuition behind lines and points in the projective plane

I've just started learning about projective plane and have trouble understand how to visualize the points and lines in the plane. Specifically, for this lemma below, when its says "all points of $l$ ...
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### A congruency proof question using circles

This is one of the last questions on a test and I couldn’t get the correct answer. The writing in red is my teacher’s, so my question is how would you prove it with the information my teacher has ...
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### prove that an equation is bounded by 1

I have an equation that is bounded by 1 and where $s<m$, how can I prove it that it actually bounded by 1. The equation is: $\frac{-m}{s}(1-\frac{s}{m})\ln(1-\frac{s}{m})$ Any help will be ...