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This problem was given as an exercise in a Functional Analysis lecture. I’ve tidied up my old solution for the problem, and here it is. Definitions Definition 1. (Sub-vector Space) Suppose that \(V\) and \(W\) are two vector spaces and \(0_V \in W \subseteq V\). W is a sub-vector space of V iff $$\forall w_1, w_2 \in W \land v \in V : v(w_1 + w_2) \in W$$ Definition 2. (Metric Space) Let \(\empty \neq X\) be a set and \(d : X \times X \mapsto \R\) be a function....

It’s quite common that when launching an application or creating a new service in the cloud, the term security comes to mind at last. Which can actually cause lots of pain; both spiritual and legal pain. In software development life-cycle (SDLC), we are most likely to put the effort into reaching the MVP or delivering the absolute must feature or fixing the regression issues. Promising to handle the security issues right after the feature/fix is delivered....

The more microservices you have the more you need asynchronous messaging between the microservices or scheduled jobs or background tasks. Background tasks are good for many reasons; lifting off the heavy load from specific microservices, run stateless jobs and scheduled tasks, asynchronous messaging etc… But failed background tasks -true to its name- can go unnoticed if you do not set up a proper monitoring or a highly available system. So you need those tasks (in short) to be fast, highly available and easy to manage....

In the intensive times at work, most of us don’t have time or energy to bother with the little details on the coding standards. But sometimes these things that we avoid chase us. When we finally end up with a spagetti code or deploying issues or environment management issues, then we take action to fix these stuff. These issues can be reduced drastically from the beginning of the projects. I will share some basic and easily applicable tips for project structure and boilerplates....

Building a Docker image with ordinary quality is quite simple. Pull an image, copy your app into the container, install the dependencies and run your program. If you’re thinking beyond just successfully ‘running’ the program, you’re at the right place. We are going to dive into the details of our image contents, reduce build time, run tests before creating the image, add functionality to Dockerfile, and ultimately create better Docker images....