Problem with the Rank of a matrix after a FindRoot

I am solving a boundary problem defined by a set of four-component vectorial functions. Without going into many details, I have two functions on the left and two on the right of an interface. The boundary problem is defined by requiring that the sum of the two functions on the left is equal to the sum of the two on the right when the functions are evaluated at the position of the interface. The various components of the functions are given by confluent hypergeometric functions of the first and second kind. A similar problem is studied in this work but with two-components functions "L. Cohnitz, A. De Martino, W. Häusler, and R. Egger, Phys. Rev. B 94, 165443 (2016) []".

The problem admits a unique solution when the determinant of the matrix associated with the 4 functions is zero. There is a free parameter $ j$ and for a given value of it, I can determine with FindRoot the associated value of the energy $ \mathcal{E}$ . For this pair of number, the determinant is smaller than $ 10^{-10}$ , however, the rank of the associated matrix is not reduced to 3 but is still 4. To reduce the Rank of the matrix, I need to work around the solution $ \mathcal{E}$ , until the determinant is not smaller than $ 10^{-16}$ !

Is there any solution around this problem. I am happy to give additional details if necessary, I am not posting the code because is pretty long at the moment.

Categorisation advice for SEO in order to rank categories [closed]

This is sort of long but probably an easy question for you all. Don’t let the text scare you, it’s an easy read.

I’m a webmaster who’s trying to set up a music store webpage. Reading about different SEO concepts and tips, and most importantly John Mueller’s famous quote on page juice, I’m currently contemplating how I may set up a long-term SEO plan for the shops webpage. Since user experience, ease of navigation and backlinks are extremely important, I have decided to implement the following for causes that will be later stated:

STEP ONE: Set up the webpage so that different categories are set up for each instrument, except an instrument of selection

STEP TWO: The page that will be getting the backlinks will be something by the line of musical instruments, which is going to be set as a category. The instrument of selection will be set as a subcategory of musical instruments, which will also be receiving lots of backlinks in itself.

STEP THREE: As the shop takes on more visitors, other instrument categories will be added to the "musical instruments" category, which will be receiving backlinks from then on. This process is repeated until most categories are taken under the umbrella of musical instruments, from which point on, the category musical instruments will be redirected to the homepage, and the instrument subcategories under it made into categories of the homepage, thus just categories in themselves.

The rationale is as follows:

Backlink building will be most focused on the main keyword, which is quite a long process, given the seo competition being very harsh where I live at, I found it would be the best of my interest to start popping up different categories ranks up one by one. I wish to gradually work my way up to the main keyword while still earning from the specific instrument categories which are easier to rank for.

Moving this way will allow me to rank for these instruments on the way to building up the main keyword backlink profile, as category pages will generate seo for subcategories and increasing subcategory numbers one by one would make it so that the umbrella term which is musical instruments isn’t too spread over the place

My issues comes into play here: How effective will this strategy be? Given that people want to view musical instruments and not "pianos" per se when they view musical instruments, I can see why people would gravitate towards the homepage, lowering screentime on page (Analysis shows "musical instruments" pages are where most people spend time and money) and thus ranks, which I PRESUME WILL LOWER RANKS FOR SUBCATEGORIES (keep in my mind early game plan is profiting from specific instruments, since ranking for musical instruments is hard in the first place). However, categorising each instrument under musical instruments would be beneficiary for the the m. inst. rank.


  1. Is there any fallicious logic behind what is written above
  2. Would screentime play part in ranking for subcategories/links that take place at the page
  3. Would category seo even help subcategories at all, does google take the websites word for what the backlink profile popularity of the page is going to affect or simply care about where users are directed towards when they visit the webpage? 4.What alternative strategies would you recommend given I want to rank for instruments as I’m gradually building up for the main keyword


How does Google rank different queries?

I’m looking for help from a backend expert or someone who can teach me more about the process search engines use to code, value, or weigh different search queries around the same topic. I also have a few specific questions about how interlinking between different sites work. I want to know if there are resources to learn more about how search engines are generally coded and developed.

I have reviewed Google’s official guidelines but am looking for something beyond Googlebots, crawlers, etc. I’m aware of the different factors that affect a site’s rankings, but I’m looking for something more technical about the algorithm itself.

Thanks for taking the time to read this; I appreciate any answers I receive.

Are any of you guys having issues getting your videos to rank on YouTube?

I have a YouTube channel with 5,000+ subscribers. In the past when I would upload a video it would take off almost immediately. Even the videos that didn't do so well would get at least 10 or 20 views per day right off the bat. That doesn't seem to be the case anymore. I recently uploaded four videos and not a single one has taken off. Has YouTube recently changed their algorithms making it much harder for videos in competitive niches to rank? I'm a little confused here.

How to rank with Pinterest?

Okay, I have figured out how to rank with Google, Yahoo, Face, Twitter and even getting hits from Instragram. All that being said, Pinterest is pissing me off LOL.

I have created two boards and posted videos as pins under the proper boards I just created. Yes, I wrote a title tag for each board and pin along with a description and has tags. It shows up on my end. However, if you click boards on the right side of the search? My boards do not appear. No, I did not click the yes button when it…

How to rank with Pinterest?