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1h
comment Expansion of terms in matrix equation
@Rajada $$g^TSr = (g^TSr)^T = r^T S^T g \neq r^T Sg$$ in general
2h
comment Expansion of terms in matrix equation
@Rajada That's only true if $S$ is symmetric.
2h
comment Expansion of terms in matrix equation
Looks OK to me. And unless you know some other properties of $S$, that's all you can do.
2h
comment Confusion between eigen value decomposition and singular value decomposition
One contains left eigenvectors of $HH^H$ vectors and one contains right ones..
3h
comment Confusion between eigen value decomposition and singular value decomposition
@Henry No, they can be different. $U$ contains the eigenvectors, and it can contain either $x$ or $-x$. Both are correct
3h
answered Confusion between eigen value decomposition and singular value decomposition
3h
comment Logic formula translation
You recieved 2 answers to your question. Is any of them what you need?
3h
comment Logic formula translation
@CᴏɴᴏʀO'Bʀɪᴇɴ There was a typo
3h
revised Logic formula translation
edited body
14h
comment Property of hermitian matrices (eigen values)
The second point follows from the first and the fact that $G^TG=G^2$.
18h
comment What are the odds of spinning matching items in a slot machine?
@GiedriusT The probability of having at least one (and possibly two) pairs and no triple is $\frac{2100}{5^5}=67.2\%$
18h
comment What are the odds of spinning matching items in a slot machine?
${5\choose 2}$ means "the number of subsets of size $2$ in a set of size $5$" in other words "the number of ways I can pick two things out of $5$ if i don't care which one I grab first." Also, made a mistake in my previous comment. I'll get back to you.
19h
comment What are the odds of spinning matching items in a slot machine?
@GiedriusT Then you can follow the same logic as for the triplets, with one more step. You have ${5\choose 2}$ ways of choosing where your pair will appear, and $5$ possibilities for what it is a pair of. The other three reels can contain anything, so $4^3$ options. However, of the $4^3$ options, you need to remove the $5$ options where a triple appears. And then, you have to divide the whole number you get by $2$, because you counted each pair of pairs twice.
19h
revised Limit of sine function
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19h
comment Limit of sine function
Also, don't get discouraged by the downvote. I downvoted the question and voted to close it because at the moment, it is not up to site standards (you have shown no work you did on your own). If you edit your question so that you show what you tried and how far you got, I will not only remove the downvote, I will add the upvote.
19h
comment Limit of sine function
Hi and welcome to the site! Since this is a site that encourages and helps with learning, it is best if you show your own ideas and efforts in solving the question. Can you edit your question to add your thoughts and ideas about it?
19h
revised What are the odds of spinning matching items in a slot machine?
added 21 characters in body
19h
comment What are the odds of spinning matching items in a slot machine?
Why. The. Hell. Did this answer deserve a downvote?!
19h
revised Prove $(a, b) \mid ((a + b), (a - b))$
deleted 2 characters in body
19h
answered Prove $(a, b) \mid ((a + b), (a - b))$