linear algebra – What is the geometric interpretation of matrix addition?

I was studying linear algebra and trying to get a visual “feel” for it through watching 3Blue1Brown’s “Essence Of Linear Algebra” series here

Essence Of Linear Algebra

Here, matrix multiplication is shown as the composition of 2 linear transformations. But I was wondering how we would interpret matrix addition/subtraction visually. I am not asking for $2$ by $1$ matrices since they would be equivalent to vector addition and subtraction respectively. But how would we interpret the addition of, say $2$ by $2$ matrices visually?

Why in Edge on Windows 10 version 20H2, when I open a link from an .exe file: in addition to the real link, an empty tab gets opened?

This happens also when I open a link from iCUE software for my many buttons Corsair mouse, and when I open a link from my OMEN SteelSeries Engine 3 many keys keyboard.

Edge is updated and Windows 10 is updated, what’s the chance that when my Windows 10 21H1 update becomes available and I install it this would be solved?

co.combinatorics – Partial orders on $mathbb{N}^m$ compatible with addition

I’m looking for a classification (or just non-trivial examples) of partial orders on monoid $mathbb{N}^{m}$ that are compatible with addition. That is, partial orders $leq$ satisfying two additional axioms:
$$forall A in mathbb{N}^{m} ;; (0, …, 0) leq A,$$
$$forall A, B, C, D (A leq B text{ and } C leq D) rightarrow (A + C leq B + D).$$

Apart from lexicographical order there exist many examples defined in terms of scalar products i.e. fix collection of vectors $v_1, …, v_k in mathbb{R}_{geq 0}^{m}$ and declare $A leq B$ iff $(B – A, v_j) geq 0 ; forall j$.

Google Sheets: How do I identify text in a column of cells and use a relative cell for addition if specific text is found?

I am looking to make a function that finds if a name (string) is in a particular cell, and then add the cell 2 columns over every time that specific name is found.

I think im looking for a type of if statement that identifies if any of cells from x to y have a specific string, then adding all the cells 2 to the right of every time the string is identified.

Specifically, I am calculating run differential in a baseball stat keeping sheet. I currently have it set up so The columns of the game logs are as follows: WINNER, LOSER, RUN DIFFERENTIAL. I am looking to create a function which finds the run differential each time that specific team played.

Example: if Team A won by 9 in their first game, the name of their team would be in the WINNER column, followed by the team they beat in the LOSER column, and then finally followed by the RUN DIFFERENTIAL (+9) which shows how much Team A, the WINNER, beat TEAM B by, the loser.

I think the idea is to first locate where the team won and lost. A team’s name in the win column indicates a win and is easy to identify, so my initial idea was to give a simple if statement for wins (If name is found in this cell, ADD the run differential which is 2 rows over, meaning they won by that much) and then sum whatever that number comes to with all the times they’re found in the loser column and the run differential of all those times, which would be how much they’ve lost by.

pathfinder 1e – Do thistle arrows deal their bleed damage in addition to the normal effects of a bow shot, or instead of it?

Thistle arrows “deal damage as a bleed effect for 1d6 rounds after a hit”. Does it cancel their normal damage, or does it essentially double the total damage dealt on the round when the arrow is shot?

Is using such arrows at least once on every potentially vulnerable enemy optimal?

time series – What effect does the addition of [“Options”] have in the following use of TimeSeries?

In an example found at Use Time Series Processing for Financial Analysis the time series

prices = sp500["PathComponent", "Adj Close"]   

is followed by

simpleReturns = TimeSeries[Ratios[prices] - 1, prices["Options"]]

to create a time series of x1/x2-1 price returns. That is the normal way to calculate price returns. But, what is the prices[“Options”] part supposed to do? TimeSeries[Ratios[prices] - 1] returns exactly the same thing. I don’t understand the prices["Options"] construction.

blending – Substance Painter: Fix color addition

Substance Painter appears to add colors together wrongly when selecting “Normal Blending Mode”

The right side is what photoshop does correctly, meaning R+G+B values in the border region never exceed 255. On the left side is what Substance Painter does incorrectly, the green dot appears to have a glow around it.

enter image description here

If there is no quick way to fix this, I will have to export Red and Green and Blue layers individually and blend them together in Photoshop.

magento2 – How can we add/register our own custom view mode in addition to default grid and list mode?

I am new to magento and using 2.4.2. I have some prior experience in working with TYPO3 CMS. Ok. Now I want to add custom table mode to the defaults (Stores -> Catalog -> Storefront -> List Mode) which needs to list the category in the table view mode.


I can understand extending something in the core is not a easy job for a beginner. I have not found any great resources regarding this topic. So kindly share some advice on what needs to be done to fulfil my requirements and provide me some references on this topic in general.

wp query – WP_Query: how to search tags in addition to a custom post type?

Below is what I have so far for a custom rest endpoint (placesdb/v1/search?term=) for a custom post type (place). This successfully returns all the places that have the search term in the title or content. However, I also want to return all the tags (tag archive pages) that match the search term. Is it possible to somehow add the tag results to the place results? I already successfully did the front-end approach of calling the places and tags endpoints separately via ajax, but I would rather get all the data in one swoop. Hence my attempt at making this custom endpoint.

function placesSearch() {
  register_rest_route('placesdb/v1', 'search', array(
    'methods' => WP_REST_SERVER::READABLE,
    'callback' => 'placesSearchResults'
function placesSearchResults($data) {
  $places = new WP_Query(array(
    'post_type' => array('place'),
    's' => sanitize_text_field($data('term'))

  $placesResults = array();

  while($places->have_posts()) {
    array_push($placesResults, array(
      'title' => get_the_title(),
      'permalink' => get_the_permalink()

  return $placesResults;
add_action('rest_api_init', 'placesSearch');

8 – How to add code that will run on visiting a URL, in addition to another module that also has code that will run on same URL, & control execution order

I’d like to make a custom module that runs code when a URL is visited and then allows an existing module with code that also runs on same URL.

So in the case of the existing module that runs on the URL, it is not affected by my module. That existing module still runs as it would in any case.

I would like my module to run first before the other module.

I’m already familiar with making a custom module and with routine, for example here: (How do I run PHP code when visiting a specific URL?))1

And I’ve seen this other answer: Override specific routing from a core module But this seems to replace the routing of another module and I don’t want to do that as said, I want my module to also run on the same URL as another module and be able to control my module running before the other. Thank you.

One thought I have so far: is the execution order of modules controlled by their order in core.execution.yml config file?


I want to run code on a callback method at the end of a 3rd-party login authentication. I believe that the callback might be a GET or POST and I’d like my code to read the values of the GET (param) or POST (form submission values) and just pass the URL call back and these intact to the original module, so it processes them as it wants as if my module hadn’t looked at them in the first place.

I want my module to look at the data in the callback as GET or POST to decide what role to give the user that’s been created and what Drupal Group for it to make to belong to, as a result of the data from the 3rd party authentication.