Thanks for the video, really helpful. had to watch it on 1.5x speed though due to my lack of patience. still, much appreciated.

Very helpful. Thank you so, so much!!

Thanks جزاك الله خيرا ❤

My Q# whether commutative property holds in subtraction of vectors

what is the meaning of associative in math? Im not a native speaker its hard to understand for me this word

This is incorrect- you do not prove that vector addition is associative, it is one of the axioms defining vector spaces.

@rachelnanshija251

8 жыл бұрын

+M that depends on your perspective. My linear algebra professor prefers to view the 10 properties as theorems, saying, "An axiom is often a “self-evident” truth. Something so fundamental that we all agree it is true and accept it without proof. Typically, it would be the logical underpinning that we would begin to build theorems upon. Some might refer to the ten properties of [a vector space] as axioms, implying that a vector space is a very natural object and the ten properties are the essence of a vector space. We will instead emphasize that we will begin with a definition of a vector space." I take this to mean that, rather than viewing a vector space as a "naturally occurring object" that math is used to describe, my professor prefers to view vector spaces as something that mathematicians define, therefore the properties must also be proved to follow from the definition proposed.

@user-lo8hn9rt1m

8 жыл бұрын

+Rachel Nanshija Your professor makes some very bold claims because even though perspective may make a difference, the logic does not follow through. He should learn the difference between a proof and a verification. I refer you to Poincaré's Science and Hypothesis for more on this matter.

@rootmath

7 жыл бұрын

It is an exercise for basic linear algebra students learning early properties of vectors with real entries. I haven't defined vector space, I've only given them vectors as objects (tuples of real numbers) and defined addition for them. In this case you can prove that the addition has all the properties of addition of real numbers without needing to assume it as an axiom. Its a simply example/exercise to build intuition. We don't need the heavy structure of a vector space for this level!

You are making a lot of assumptions that does not hold true for many spaces