the matric

Why on earth is matrix multiplication NOT commutative ? – An Intuition

One is commonly asked to prove in college as part of a linear algebra problem set that matrix multiplication is not commutative. i.e If A and B are two matrices then :

But without getting into the Algebra part of it, why should this even be true ? Let’s use linear transformations to get a feel for it.


If A and B are two Linear Transformations namely Rotation and Shear. Then it means that.

Is that true? Well, lets perform these linear operations on a unit square and find out:

(Rotation)(Shearing)

(Shearing)(Rotation)

You can clearly see that the resultant shape is not the same upon the two transformations.

This means that the order of matrix multiplication matters a lot ! ( or matrix multiplication is not commutative.)

Have a great day!

Basis Vectors are instructions!

Basis vectors are best thought of in the context of roads.

Imagine you are in a city - X which has only roads that are perpendicular to one another.

You can reach any part of the city but the only constraint is that you need to move along these perpendicular roads to get there.


Now lets say you go to another city-Y which has a different structure of roads.

In this case as well you can get from one part of the city to any other, but you have to travel these ‘Sheared cubic’ pathways to get there.

Just like these roads determine how you move about in the city,

Basis Vectors encode information on how you move about on a plane.


What do I mean by that ?

The basis vector of City-X is given as:

This to be read as - “ If you would like to move in City-X you can only do so by taking 1 step in the x-direction or 1 step in the y-direction ”


The basis vector of City-Y is given as:

This to be read as - “ If you would like to move in City-Y you can only do so by taking 1 step in the x-direction or  1 step along the diagonal OB ”


Conclusion:

By having the knowledge about the Basis Vectors of any city, you can travel to any destination by merely scaling these basis vectors.

As an example, lets say need to get to the point (3,2), then in City-X,  you would take 2 steps in the x-direction and 3 steps in the y-direction

And similarly in City-Y, you would take 1 step along the x -direction and 2 steps along the diagonal OB.

Destination Arrived :D

7

POWER OF THE PRIMES!

IS!

HERE!

Prime Master Liege Maximo (Skullgrin)! These tiny TFs represent the Sparks of the Thirteen Original Transformers and can ride around in Legends class figures, become the heads (or power-ups?) for Deluxe or Voyager toys, or become one with the matrices of Leader Class figures!

Legends Class Beachcomber! Peeps can ride him!

Deluxe Class Dreadwind! He can combine in vehicle mode with Blackwing (nee Darkwing, not pictured) into Dreadwing, just like 1988! He’s also built off Combiner Wars Skydive, and it looks like he can still become an arm or leg!

Deluxe Class Jazz! Is that a Combiner Wars peg in his chest? Maaaaybe!

Voyager Class Starscream! … nobody really knows what his deal is yet. Is he a new combiner torso? We hope!

Leader Class Evolution RODIMUS PRIME! Turn a Deluxe-scale Hot Rod into a car, wedge him into his trailer, or combine him with his trailer into Rodimus Prime! His removable Matrix has a removable crystal, into which any Prime Master can be inserted! Will this gimmick carry across the entire size-class? Apparently so, as they all have their own matrices, and evidence also points to them all ALSO being small dudes who merge with things to get bigger…

… ~and that even includes Optimus Primaaaaaal, who won the Power of the Primes fan vote!~

LEADER CLASS SELF-COMBINING OPTIMUS PRIMAL

PEACE OUT

anonymous asked:

Why do you hate the idea of "internalized anything? "

It’s a silly way of understanding marganilization in my opinion. Interactions take place within matrices of marginalization and material relations- the identities of the people engaging in the interactions are important but not terribly so, and certainly they are not so separable that they need their own term. So for instance, let’s say a black woman passes me by for a job and gives it to a white woman who’s less qualified, just because of things she assumed because she is black. The interaction between us takes place under the matrix of racism (I am denied access to material resources specifically due to my race) and that wouldn’t change if the woman denying me the job was Latina, or white- either way, my NOT being white and that being the determining factor here makes the interaction racist. Calling this an instance of “internalized racism” not only shifts the focus to that woman’s particular feelings (which honestly, they matter but in the whole scheme of the interaction, I don’t care) but also makes it seem as though this racism exists inside her, and is a personal problem, and not the result of being born and baptized in a racist system which has tainted her worldview. So had a white woman done the same thing, she would also be doing it because she had “internalized” the logics of racism- we all “internalize” these logics and have to work toward seeing them as ideology rather than truth. Racism isn’t internal, it’s external, and racist interactions occur within it- not just between individuals. Of course we should have special sympathy for people of color who seem especially impacted by racist thought in a way that makes them hate themselves. But for one thing, they aren’t internalizing anything that other people don’t (it just hurts other people less because it isn’t about them) and for another, we need to focus on the system at work.


I get the idea, I really do. And I sympathize with it. I do think women enacting misogyny in our interactions with each other comes from a different emotional place than when men do the same thing, and I think this deserves recognition. But at the end of the day, one woman not “internalizing” misogyny doesn’t make patriarchy go away. So I’m not terribly interested in the idea that marginalized people’s interactions with systems are different in this particular sense- they’re not really, but we stand to be hurt a whole lot more by them than people who aren’t the targets of those systems. I think a lot of my reaction is just visceral, a reaction to this idea that the problem lies within a particular person rather than in broad material structures. It feels nice, but doesn’t hold much political weight.

2

DAY 6/100 OF PRODUCTIVITY // DAY 1 OF APRIL STUDY CHALLENGE // 1 APRIL 2017

HEY ITS APRIL. i napped for the entire afternoon after math tuition because i was so shagged. but kinda made up for lost time at night, did my matrices notes at abt 1am. so i was pretty productive. but body clock messed up hahaha

so, “what’s going on this month?” i’ve got a batam trip on the 14th to i think 16 april. and after that i have my O level bio SPA so stress!! but there r other days like careers day (7th) to see polytechnics and JCs in our school for talks and i think that’s abt it actually.

gonna sleep now (it’s almost 4am) so i can get up at abt 9-10am (hopefully) and get my life back on track by finishing up my homework for school and tuition for tomorrow afternoon (i still have like half of it to finish)

goodnight everyone and i hope y'all had a great 1st april. oh and happy april fools!

xo,
Pre [@konstanly-studying]

anonymous asked:

Since you're the one who made me see matrices everywhere: What about Optimus Primal's chest shape for Onyx's matrix? Or Micronus' weird tummy for his matrix? And since Prima's matrix is part of his artifact, the Enigma of Combination and one of the two versions of the Forge of Solus being Nexus and Solus' matrices respectively? (Your designs are really cool, and this is basically my way of going a little gaga over them. Your writhing, skittering Unicron is really disconscerting to look at!)

Legit though I love designing Matrices? It’s so weird and neat to try and figure out what shapes make for a good matrix!

Here’s some in-canon matrices because I have these pictures saved anyways.

By no means is this an extensive selection of Matrices but I definately want to revisit my Matrix designs to make them more varied in appearance or at least try to make some of them wilder!

2

day 60 of 100 days of productivity
woah guys sorry for the massive break i’ve been doing stuff and i’ve been tired and i haven’t actually needed to do any work bar my geography project which was just in classes. i’m possibly going to be finishing up 100 dop this summer if i work everyday wahey !!!!!

Lo so,
non esiste una dimensione assoluta, una verità universale.
Eppure sento, che anche essendo individui a sè, separati, pur non volendo emulare nulla, ci portiamo dentro l'istinto, l'essenza dei nostri padri, delle madri e qualcosa di chi li ha preceduti.
La vita, a prescindere da ogni tentativo di comprensione, il segreto, la matrice dell'esistenza.
Le luci e le ombre, i misteri inesprimibili, i sogni, dove forse è nascosta la chiave di lettura di tutto il nostro essere vita