#vectormath — Public Fediverse posts

Alright, future engineers!
**Dot Product:** A scalar value indicating how much two vectors point in the same direction.
Ex: For `u=[1,2]`, `v=[3,4]`, `u.v = (1*3) + (2*4) = 11`.
Pro-Tip: If `u.v = 0`, the vectors are orthogonal (perpendicular)! Key for geometric analysis!
#VectorMath #LinearAlgebra #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar value indicating how much two vectors point in the same direction.
Ex: `v · w = v1w1 + v2w2` (for 2D).
Pro-Tip: If `v · w = 0`, the vectors are orthogonal (perpendicular)! Key for projections.
#LinearAlgebra #VectorMath #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar product measuring how much two vectors point in the same direction.
Ex: `u . v = u1v1 + u2v2 + ...`
Pro-Tip: If `u . v = 0`, the vectors are orthogonal (perpendicular)!
#LinearAlgebra #VectorMath #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar value measuring how much two vectors align.
Ex: For `v=[1,2]`, `w=[3,4]`, `v.w = 1*3 + 2*4 = 11`.
Pro-Tip: If `v.w = 0`, the vectors are orthogonal (perpendicular)!
#LinearAlgebra #VectorMath #STEM #StudyNotes

**Linear Independence:** A set of vectors is independent if no vector can be written as a linear combination of the others.
Ex: For `v1, v2`, if `c1v1 + c2v2 = 0` implies `c1=c2=0`.
Pro-Tip: Essential for defining a basis & ensuring unique solutions in matrix equations!
#LinearAlgebra #VectorMath #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar value showing how much two vectors point in the same direction.
Ex: For `u=(u1,u2), v=(v1,v2)`, `u.v = u1*v1 + u2*v2`.
Pro-Tip: If `u.v = 0`, the vectors are orthogonal (perpendicular)!
#LinearAlgebra #VectorMath #STEM #StudyNotes

Alright, future engineers!
**Linear Independence:** Vectors are LI if none can be formed by combining the others.
Ex: `v1, v2` are LI if `c1v1+c2v2=0` means `c1=c2=0`.
Pro-Tip: LI vectors add new information & are key for a basis!
#LinearAlgebra #VectorMath #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar value representing how much two vectors point in the same direction, or the projection of one onto another.
Ex: `[1,2] . [3,4] = 1*3 + 2*4 = 11`.
Pro-Tip: If their dot product is zero, the vectors are perpendicular! Essential for geometric understanding.
#LinearAlgebra #VectorMath #STEM #StudyNotes

Alright, future engineers!
**Dot Product (Scalar Product):** Multiplies two vectors to give a *scalar* measuring their directional alignment.
Ex: `[1,2] . [3,4] = 1*3 + 2*4 = 11`.
Pro-Tip: If `a . b = 0`, the vectors are perfectly orthogonal (perpendicular)! This is KEY for geometry & projections.
#LinearAlgebra #VectorMath #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** Measures how much two vectors align, producing a scalar.
Ex: `[1,2] · [3,4] = (1*3)+(2*4) = 11`.
Pro-Tip: If it's zero, vectors are orthogonal! Essential for projections & angles.
#VectorMath #LinearAlgebra #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** Measures how much two vectors align; it's a scalar value.
Ex: For `A=[1,2]`, `B=[3,4]`, `A.B = (1*3) + (2*4) = 11`.
Pro-Tip: If A.B = 0, vectors are orthogonal (perpendicular)!
#LinearAlgebra #VectorMath #STEM #StudyNotes

Alright, future engineers!
**Dot Product (v⋅w):** A scalar measuring how much two vectors point in the same direction.
Ex: For `v=[1,0], w=[0,1]`, `v⋅w = 1*0 + 0*1 = 0`.
Pro-Tip: If `v⋅w = 0` (and `v,w` non-zero), they're ORTHOGONAL! Key for projections & geometry.
#VectorMath #LinearAlgebra #STEM #StudyNotes

Alright, future engineers!
**Dot Product:** A scalar value from two vectors, representing their similarity or alignment.
Ex: For `v=<a,b>`, `w=<c,d>`, `v.w = ac + bd`.
Pro-Tip: If `v.w = 0`, the vectors are orthogonal (perpendicular)!
#LinearAlgebra #VectorMath #STEM #StudyNotes

Alright, future engineers!
The **Norm** (`||v||`) is the length or magnitude of a vector. Ex: For `v=[3,4]`, `||v|| = sqrt(3^2 + 4^2) = 5`. Pro-Tip: Essential for calculating distances & normalizing vectors to unit length!
#LinearAlgebra #VectorMath #STEM #StudyNotes

Alright, future engineers!

A **Linear Combination** is a new vector made by scaling existing vectors & adding them. Ex: `2*[1,0] + 3*[0,1] = [2,3]`. Pro-Tip: It's the fundamental way to build new vectors within a given space!

#LinearAlgebra #VectorMath #STEM #StudyNotes

Alright, let's nail this Linear Algebra concept!

Dot product measures how much two vectors 'agree' on direction. Ex: For v=[v1,v2], w=[w1,w2], v.w = v1w1 + v2w2. Pro-Tip: If v.w = 0, they're orthogonal! Crucial for projections & bases.

#LinearAlgebra #VectorMath #STEM #StudyNotes

Piotr Migda tries to explain vector math magic in 'king – man + woman = queen' using #word2vec 🤓, but it's basically just a linguistic Ouija board session. 🤔 Spoiler alert: it's still math, not #sorcery. 🧙‍♂️✨
https://p.migdal.pl/blog/2017/01/king-man-woman-queen-why/ #PiotrMigda #vectorMath #linguisticOuijaBoard #mathNotMagic #HackerNews #ngated

FYI: Vector Search Magic: Superhero & Sporty Car Combo! #shorts: By using vector math, one can combine a DeLorean image with the text query for superhero to generate an embedding. Averaging these embeddings together then allows a search to find a superhero on top of a sporty car with cool lights. #vectormath #image #superhero #DeLorean #embedding https://www.youtube.com/shorts/RMX2A02pP90

ICYMI: Vector Search Magic: Superhero & Sporty Car Combo! #shorts: By using vector math, one can combine a DeLorean image with the text query for superhero to generate an embedding. Averaging these embeddings together then allows a search to find a superhero on top of a sporty car with cool lights. #vectormath #image #superhero #DeLorean #embedding https://www.youtube.com/shorts/RMX2A02pP90

Vector Search Magic: Superhero & Sporty Car Combo! #shorts: By using vector math, one can combine a DeLorean image with the text query for superhero to generate an embedding. Averaging these embeddings together then allows a search to find a superhero on top of a sporty car with cool lights. #vectormath #image #superhero #DeLorean #embedding https://www.youtube.com/shorts/RMX2A02pP90

#100DaysOfCode day 13:
A bit to much beer and a little late to sleep last night, so not much done today, but I did continue with some #vectorMath and #NatureOfCode, today it was multiplication.
#Javascript #CreativeCode #GenerativeArt #Math

https://editor.p5js.org/mhoumann87/full/K1p17fPdM

#100DaysOfCode day 11:
More of the same. #vectorMath in #P5JS. Made a random walker that uses a velocity random vector. And I am pretty happy about that, took some searching on the web, but finally got the right result.
#Javascript #CreativeCode #Math #generativeArt

https://editor.p5js.org/mhoumann87/full/eKRBJEmpL

#VectorMath #GodotEngine #Help

Can anyone explainify a thing to me?

See : https://docs.godotengine.org/en/3.0/tutorials/math/matrices_and_transforms.html

There's a part where they say:

"This was expected, but then let’s do something more interesting. Use the dot product of X and the point, and add it to the dot product of Y and the point:
var final_pos = Vector2(x.dot(new_pos), y.dot(new_pos))"

And I can hear the point wooshing over my head. They also say they explained it before, but I can't find that 'splain.

Halp!
🦇

Looking for good resources on rasterizing 3D to 2D.

Use case is a game that sends PNG images of a view of a system.

The view is from a player's perspective. I have their x,y,z, the x,y,z they're observing, their field of view.

I'm stuck at how to determine the plane this view projects on.

I know the distance between observer and the one point on that plane but don't understand how to make a plane perpendicular to the line.

#Geometry #Trigonometry #VectorMath #3DRender

Good stuff about 2D collision detection.

https://timallanwheeler.com/blog/2023/01/27/2d-player-collision-against-static-geometry/

#gamedev #collisiondetection #vectormath #programming