/sci/ - Science & Math

a + 0 = a
a + b = b + a
(a + b) + c = a + (b + c)
a + (-a) = 0
a * 1 = a
a * b = b * a
(a * b) * c = a * (b * c)
Given a != 0, then a * 1/a = 1

ax + bx = (a + b)x
x^a * x^b = x^(a + b)
(x^a)^b = x^(ab)
If xy = 0, then x = 0 or y = 0

Here you go. No need to read that book. Just memorize that top group of rules, and if you're feeling up to it, the second group as well, but they can just be derived, so they're really not as important.

>>8529856
>a * b = b * a
[eqn]
\begin{aligned}
\begin{bmatrix} 1 & 2 \\ 3 & 4\end{bmatrix} \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} &= \begin{bmatrix} 19 & 22 \\ 43 & 50 \end{bmatrix} \\
\begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} &= \begin{bmatrix} 23 & 34 \\ 31 & 46 \end{bmatrix}
\end{aligned}
[/eqn]

>>8529868
>matrices form a non commutative algebra
>in other news water is wet

>>8529873
>noncommutative
[eqn]
\begin{aligned}
AA^{-1} = A^{-1} A &= I
AI = IA &= A
\end{aligned}
[/eqn]

>>8529873
pretend my post >>8529878 had the proper line break pls

>>8529571
dude algebra is just u do one thing to an equal thing u do another same thing to the other and their equal
u needa crawl for ur ball

>>8529880
I can forgive an improper line break, but not an assertion of a false proposition!
[math]AA^{-1} = IAI[/math]
Explain yourself!

>>8529878
rofl you are dumb hahahaha
there exists a subset of matrices that actually commutate, yes. But for a algebra to be commutative you need ALL matrices to commutate with each other.

>>8531102
>rofl you are dumb hahahaha
Was that part really necessary?

>>8531106
>Was that part really necessary?
its 4chan mate, deal with it or fuck off

>>8529868
>>8529878
>>8531099
Take your pedophile cartoons back to >>>/a/

>>8531113
heh, you showed him m8.