“Show don’t tell” but how?

Write abstract things as if you can see them, touch them! A good start is to remove abstract words from your writing.

Good writing engulf you. Words are no longer a words, they turn into images, sounds, dreams, melancholies. By definition an abstract noun can’t be perceived with our senses which means it can’t activates the mind’s eye. Instead of describing physical things, they represents qualities,state or feelings Close your eyes and try to imagine “beauty”. I bet that you imagined a real word object you found beautiful. Might be beautiful visage, a flower, a painting… We’re wire for the concrete and our only way to comprehend the abstract is to convert into the concrete. Facilitate the life of you reader then, Avoid abstract noun Happiness Justice Honesty One tip to catch them: they often originate from adjective through a process called nominalization.

What’s the fuck is this?

What’s the fuck is this?

What’s the fuck is this?

We often normalize direction vectors to create unit direction vectors, which have a magnitude of exactly 1. The unit direction vector is calculated as $\hat{v} = \frac{\vec{v}}{|\vec{v}|}$, where $|\vec{v}|$ represents the magnitude of vector $\vec{v}$.

Unit direction vectors are particularly useful because they specify pure direction without any magnitude information. This allows us to separate the concepts of “which way” and “how far,” making calculations cleaner and more intuitive. When we need a vector in a specific direction with a particular magnitude, we can simply multiply the unit direction vector by the desired scalar value.

The process to solve Ax=b involves 2 steps. Reduce the matrix to lower triangular form. The back substitution.

If you keep track of all the elimiation matrix you needd to apply to A for it to become lower triangular,

What does it means to be going in the same direction. If we were both walking in the same room with you, I’m sure you could determine intuively wheter we’re going in the same direction. How can we catch that intuition precisely. We give coordinate to our space using the cartesian plane. What’s the difference between these two sets of vectors:

If you imagine the unique line on which a vectors lies, We are on the same direction if we are on the same line [[]]

If you interrogate the formula for the dot product, it will gift to you all the explanations you need. You’ve seen mathematicians define the same dot product in different ways.

The geometric definition of the dot product

In the two dimensional plane, start wit two vectors at the origin. Just think of our vectors as line segment that draw starting at coordinate (0,0)–your origin. The dot product of those two line segments(vectors) equals u.v = costheta times length u times lenght v

Have you heard the phrase “X is a markup language” where X could be HTML, Markdown, LaTeX, or XML? But what exactly is a markup language? Let’s do a thought experiment. Imagine that you’re a busy author who writes books but don’t want to have to format the book yourself. You don’t want to worry about the table of contents, the page numbers, the footnotes, the bold words… So you engage a publisher that will format your book properly.