invertible matrices are positive definite?

If a matrix appears as $A=B^{-1}$, is it automatically positive definite?

Invertible matrices have full rank, and so, nonzero eigenvalues, which in turn implies nonzero determinant (as the product of eigenvalues).

How to Stay Positive When It Feels Like Your Life is Falling Apart

  1. apexis





    Apr 16, 2012
    Likes Received:

    How to Stay Positive When It Feels Like Your Life is Falling Apart

    1. Be Grateful

    Even if it seems everything is going wrong, there are things that are going right. Every day, write down all the things you are grateful for having happened to you today. Be descriptive of each item. Feel the joy those things bring you. Even if it’s something really small like your car started this morning. Be grateful for it. This will help you to stay focused on the positive.

    2. Look for the Silver Linings

    Sometimes events that initially look bad turn out to be really good things in the end. I can’t remember the saying but it was something like every black cloud has a silver lining. Here’s an example, maybe you need to look for a new job because your company is downsizing. If you look for the silver lining in that, you can see that it’s making you leave a job you didn’t like that much anyway. You can now find that job that you really want to do or pursue a lifelong dream or even just take some time off to enjoy life before going back to find another job. By looking for the silver lining then bad things can actually become really good things.

    3. Often the Greatest Doubts Occur Just Before a Breakthrough

    This is a quote by Lama Surya Das. If you can think of your difficulties as being necessary to make a breakthrough to the new life you want to lead, it will make it easier. You’re breaking free of your old life on the way to your new, more exciting life.

    4. Look at the Big Picture and Focus

    Decide on what direction you want your life to head. Think about what areas you want to explore, what experiences you want to feel, what do you want to accomplish in your life? What kind of person do you want to be? Then start taking steps towards those goals. Even if it’s just tiny steps every day, stay focused on where you want to go, and keep moving forwards. Then the little things you’re going through right now won’t matter as much because you have an exciting new direction to focus on instead.

    5. Discouragement is Just a Trick

    Here’s a quote I really like about not letting yourself get discouraged. “Discouragement is a negative emotion with more than one trick up its dark sleeve. It tricks you into mentally or emotionally dwelling in the very place you want to leave. Drop all such sorrow permanently by daring to see through this deception of the nconscious mind. You have a destination far beyond where you find yourself standing today” – Guy Finley Keep this in mind as you continue to take steps towards your goals. You do have a destination far beyond where you are today.

    6. Keep Reading Inspirational Articles and Maybe Join a Forum

    If you keep reading inspirational articles and books, it will motivate you to stay positive. You will see that everyone goes through rough patches but that they do make it through. It will be worth it in the end. Also, there are some good forums you can join where even just reading the other posts can motivate you to stay positive. Or, if you want to make a posting, you can gain support from others as well. Who knows, you may even be able to answer some one else’s post and help them out too.

    7. Take a Break Sometimes

    Forget about your problems and just go out and do something fun. Go to a movie, go out with some fun, positive thinking friends, go to a play, go for a bike ride, just do something. Get out and just enjoy yourself for a little bit. Sometimes, we just get so wrapped up in our problems that we forget to have fun. Taking a break will re-energize you and you may find that things aren’t as bad as you thought.


  2. diggersjohn33

    Dec 22, 2011
    Likes Received:

    Point #1 is a biggie for me.

    If you believe, you can achieve.


  3. clickfund

    Aug 29, 2012
    Likes Received:

    This is a great post, so true that you can make things boulders on the beach or pebbles in the sand


  4. Amanda@Mindsettable

    Jun 28, 2020
    Likes Received:

    I really like your points, and I think when things really seem tough, #3 is especially good to keep in mind.


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number theory – For any positive integer $k$, there exists a prime $p$ such that ${x choose k}equiv -1pmod{p}$ has an integer solution.

Here is a conjecture of mine. Prove that for any positive integer $k$, there exists a prime $p$ such that $${x choose k}equiv -1pmod{p}$$ has an integer solution.

When $k$ is odd, we can take $x$ to be $p-1$, the question can be easily solved because $${p-1 choose k}equiv (-1)^kequiv -1pmod{p}.$$ However, when $k$ is even, I cannot find any pattern. Here are results for $k=4$ and $k=6$.

$$x=30implies {x choose 4}equiv -1pmod{193},$$
$$x=34implies {x choose 6}equiv -1pmod{97}.$$

It Just Feels Good to Be Positive

Your attitude can really make a difference in the outcome of various situations in your life. The way you approach the things that go on in your daily walk can really impact you in ways you might not have thought about. Imagine you are going along your normal routine and you encounter a challenge along the way. How you handle that particular challenge can really mean the difference between a success and a failure.
Being positive in the time of a challenge can really help make your life easier. You can experience less stress because your mindset is set on positivity and not negativity. There’s just something about being negative that drains all of your energy right out of you and puts you in a horrible frame of mind and mood which is not healthy. Being positive releases less stress and puts your mindset in one of a “can do” attitude which results in better results and not being stressed out. It’s amazing how a simple smile or laugh can change your attitude. When I am faced with a challenge, sometimes I just break out into laughter. Sometimes you have to laugh to avoid crying or being upset. It has really helped, plus when you frown, you get more wrinkles (smile).

The next time you are in a stressful situation or life just happens, take time to make every effort to keep a positive mindset in your daily walk. It can make you more productive and reduce stress. Have a wonderful day!


modular arithmetic – Any easier way to get the quotient and remainder from a minus number divided by a positive one?

negative number divided by positive number, what would be remainder?

I’ve read these answers linked above, but I don’t feel I’m answered enough.
$$-27 = underbrace{-6}_qcdot underbrace{5}_d + underbrace{3}_r$$
They say this, but I don’t think I can use it later when I need to divide some large minus number with another large positive number, such as -777777 with 439. Positive number division is easy enough that no matter how young you are, even grammar school students could solve it with enough time given. I was wondering if there’s any that kind of easy method to get the quotient and remainder from the minus numbers divided by the positive numbers.

Positive – My honest review of B3 Hosting | NewProxyLists

First of all I want to tell you this is my honest review of B3 Hosting.

I did not get paid for this review, nor I’m affiliate, the owner or connected with the company by any means, so don’t give me BS that I’m doing this for money or whatever…it’s a pure honest review from a guy that has tried over 50 hosting providers throughout the world in the past 20 years.

Now let’s get into subject…

I got my first contact with this company through a friend from France who’s a bettor (like me) and owns a sports tipsters website. I needed a dedicated server for my e-store…I have a massive database with tens of thousands of products and I was looking for a dedicated server anywhere in Europe. I wasn’t looking for cheap, unreliable server that could break when first order was made.

I initally had about 3 poor tries with larger companies from UK, France and Czech Republic and I wanted to try something different. I wasn’t looking for an appartment hosted server either, but I wasn’t looking for some jumbo hosting company that would have me waiting 48 hours to answer a bloody ticket if needed.

Therefore I decided to go on with the advice of my friend (who by the way, has an amazing website with over 10000 active users and has a shared hosting that pays less than 15 USD/month, which is amazing if you ask me).

I looked at their website, seemed really pro, which was a great first impression. Secondly looking at prices for dedicated servers, really liked the fact that there’s a lot of options and they have you the option to configure your own server (adding as many RAM as you need or SSD and removing/ adding more features, as requested), which is something most jumbo providers don’t allow.

Then I decided to contact the customer representative to see if I can get a better deal if I had paid a server for 1 year in advance (TIP: It doesn’t say anything about that on dedicated servers page, but if you really can afford to pay in advance for 1 year, you will get a good discount). You can see on all other pages that there are up to 50% discounts for paying in advance VPS servers, shared hosting or wordpress hosting, but nothing on dedicated servers, however if you ask the customer support, they will provide you a discount.

I personally got a 20% discount for paying a server in advance so instead of paying 139 EUR/month, I ended up paying 111.2 EUR/month, which is really great for 12 Cores, 32GB RAM with 240GB SSD and guaranteed 500Mbps internet…unlimited traffic, of course…

I was more than satisfied with the fact that they even helped me migrate my website even if I didn’t need it, and now my website runs faster than ever. I get reply to my tickets very fast (in about 1-2 hours at most) and I’ve even paid 50 EUR/month for one of their guys to manage my server for me…I mean what can you ask for more?

I’m already with them for about 11 months and looking to ask them to buy 2-3 more years (maybe I’ll get an additional discount – Wish me luck 😀 )

To put it shorter here are the:


Answering time for tickets is really fast (never had a ticket that didn’t have an answer in less 2 hours at most) – They claim 24/7 technical support, which is correct in my case.

They have many datacenters so you can host your website/server in either Romania, France, UK, or Germany. As far as I understand from them, they’re planning to open another datacenter (or to parter with a company with a datacenter) in South Africa, US, Australia and Canada.

Massive discounts when paying for 1 year upfront (up to 50% on some services)

Many payment processors accepted (PayPal, credit/debit card, cryptocurrency) and I think they also accept Skrill, Neteller, but I’m not 100% confident about that

According to pagespeed and gtmetrix both my website and my friends website are about 25-30% faster than the old hosts we had, so I personally don’t mind at all :)


Live chat is only available during working hours in Romania (GMT +2), so all commercial, technical and sales question have to be sent via ticket if not during working hours ( Monday – Friday: 09:00 – 18:00, Saturday: 09:00 – 13:00 GMT +2). Not a big deal for me, but some people want live chat support.

Website is only in Romanian and English (sorry my French friends)

Small team of experts…as far as I understand they have less than 20 people in the company…for some may seem a lot, but they’re still a small company compared with jumbo giants. I don’t mind about that, because I was actually looking for smaller company to form a relationship.

In conclusion, if you’re looking for a small serious company that can provide you top class hosting, you can give B3 Hosting a shot. As far as I saw on Google search there are more B3 hosting companies, but I’m recommending the one from Romania ending with .ro domain name. Prices are more than decent, you can get great discounts for paying in advance and the support is awesome. If you want no headaches you can pay 50 EUR/month and tech guys will take care of all server issues for you, offering you 24/7 + phone support any time, so you can rest assured your business is up and running always.

Thank you for your time and let me know if you have any questions about them….I would answer as far as my knowledge about them goes.

Let me know in the comments if other people have tried them and what’s their opinion about them!

real analysis – Flux through the positive part of a sphere centered at $(0,0,1)$

Let $$B={(x,y,z):x^2+y^2+(z-1)^2<4, zgeq 0}$$ and consider the vector field $$F:(x,y,z)mapsto(x^3,y^3,z)$$

I want to compute the flux of $F$ through $partial B.$

We have $$text{Div}F=3x^2+3y^2+1$$ and so by the divergence theorem we could compute the flux as $$int_B 3x^2+3y^2+1 dx dy dz$$
but this triple integral does not look very friendly to me using spherical coordinates, because the sphere is centered in $(0,0,1).$

Another approach is by computing $$partial B ={x^2+y^2leq 3, z=0}cup{x^2+y^2+(z-1)^2=4, z>0}$$

I can parametrize ${x^2+y^2+(z-1)^2=4, z>0}$ as $$x=2sin phi cos psi$$ $$y=2 sin phi sin psi$$ $$z= 2 cos phi +1$$ $$phiin(0,pi), psi in (0,2 pi)$$ but it does not seem to make calculations easier.

For infinitely even positive integers k for which ϕ(n)=k has no positive integer solution

Show that for infinitely even positive integers k for which ϕ(n)=k has no positive integer solution n

Worldstream review (positive) | Web Hosting Talk

I moved to Worldstream at start of 2019 after trying some host which was really terrible that was reselling worldstream (i got the impression the dedi wasn’t dedi and shared or the equipment was not what i was sold) so i thought why not try the source (worldstream) instead of using this reseller.

Have to admit the reviews of Worldstream weren’t very positive here (not sure why) but i was pretty desperate at the time trying anything and i ordered worldstream. The server was delivered and i was impressed. Everything was as advertised including the 1gbit port. Well, it’s not really impressive but considering the fraud of hosts i had just tried, i was pleased to see what they advertised is what was sold.

I have now 3 dedicated servers with them in the span of 18 months and i have nothing but praises for them.

Was lucky to grab a beast of a machine that they now offer at a more expensive price but their prices are the best and i haven’t seen such equipment with so cheap prices on other hosts. They are slowly increasing pricing though and in 2019 they were offering a lot cheaper. I guess prices increased due to the pandemic?.

Downtime wise, it’s not a 100 percent uptime, the server would shut off for no reason and i couldn’t figure out why. Not really sure if it was worldstream server fault or some malicious traffic crashing apache server. It was rare and has happened like 2 or 3 times in 18 months. There was like brief few minutes (10-15 minutes) network slowdowns a couple of times. But this is really nothing bad or out of ordinary, the uptime would be 99.99% and 2020 has been rocksolid with 100% uptime!.

Support is the fastest i have seen. I received a response within 5-15 minutes and it’s not automated gibberish either. Even the technical support team responds quick which other hosts take hours/days to respond compared to non-technical requests.

These are really the most important points for me with a host and i am really happy. Hope they continue being this awesome for years and don’t suddenly go down in quality like some other hosts do especially their superb prices.

I highly recommend them. In fact, i wish i had found them earlier. The crappy expensive VPSes I tried, they sell a dedicated for the same price.