Anonymous at Fri, 18 Oct 2024 16:47:45 UTC No. 16438202

>>16436360
no

Anonymous at Fri, 18 Oct 2024 17:33:13 UTC No. 16438299

These are definitions for me

Anonymous at Fri, 18 Oct 2024 17:44:47 UTC No. 16438322

>>16436360
I was just thinking there should be a linear algebra thread in /sci/ since it's so fundamental in science, tech and engineering.

I can prove almost all of those, except the ones dealing with orthogonal complements and eigenvalues. I'm doing a second pass on linear algebra writing notes in spanish and I still don't go through inner products and eigenvalues.

Anonymous at Fri, 18 Oct 2024 18:24:38 UTC No. 16438377

>>16438299
yes, but you can prove that all those definitions are the same, as in you can go from any one to any other one

Anonymous at Sat, 19 Oct 2024 02:10:34 UTC No. 16439133

>>16436360
I probably could but it would take hours.

Anonymous at Sat, 19 Oct 2024 02:14:20 UTC No. 16439138

>>16436360
I think a handful are pretty aids to prove for how elementary they are like the proof covers 2-3 pages
at least from what I remember from a book that presented it the same way

Anonymous at Sat, 19 Oct 2024 10:30:50 UTC No. 16439518

>>16436360
Anyone with an IQ above whatever can derive 2 or 3 of 5 these himself, but it’s literally a completely worthless skill to find this shit intuitive.
Like, I study philosophical logic for crying out loud, which I find intuitive.

Anonymous at Sat, 19 Oct 2024 12:18:41 UTC No. 16439603

>>16439518
>but it’s literally a completely worthless skill to find this shit intuitive.

Anonymous at Sat, 19 Oct 2024 12:29:26 UTC No. 16439613

>>16439603
fag

Anonymous at Sat, 19 Oct 2024 12:54:35 UTC No. 16439644

>>16439613
imagine getting filtered by linear algebra

Anonymous at Sat, 19 Oct 2024 14:58:00 UTC No. 16439803

>>16439518
I use basic UG LinA concepts every day on the job. It's not worthless in some fields.

Anonymous at Sat, 19 Oct 2024 15:07:01 UTC No. 16439813

Is this OP Barkon? Seems so. Isn't he banned?

Anonymous at Sat, 19 Oct 2024 15:24:50 UTC No. 16439835

>>16436360
Von Neumann discovered (invented) most of these things.

Anonymous at Sat, 19 Oct 2024 17:13:03 UTC No. 16439982

>>16439835
are you saying he was smarter than me? seems unlikely

Anonymous at Sun, 20 Oct 2024 14:37:43 UTC No. 16441236

>>16436360
>420 proofs
anyone can do this. i'm not going to though, faggot

Anonymous at Sun, 20 Oct 2024 17:53:38 UTC No. 16441431

>>16441236
i think if you just prove any one of those once to a), then you can chain the proofs from any to any other one

Anonymous at Sun, 20 Oct 2024 18:21:51 UTC No. 16441470

From which axioms.

Anonymous at Sun, 20 Oct 2024 22:55:55 UTC No. 16441820

>>16441470
the axioms of linear spaces, dumbass

Anonymous at Sun, 20 Oct 2024 23:28:56 UTC No. 16441868

>>16441236
you mean 22

Anonymous at Mon, 21 Oct 2024 02:29:25 UTC No. 16442066

>>16441868
I think you can get away with 21 since there are 21 statements
with 3 statements you need to prove a -> b and b -> c and c -> a

Anonymous at Mon, 21 Oct 2024 02:39:48 UTC No. 16442075

>>16438202
/thread

Anonymous at Mon, 21 Oct 2024 02:42:34 UTC No. 16442076

>>16439813
He is using his boyfriend's internet again.

Anonymous at Mon, 21 Oct 2024 21:16:06 UTC No. 16443102

>>16436360
yes

Anonymous at Tue, 22 Oct 2024 02:18:30 UTC No. 16443472

>>16436360
Starting from a), and going down to u)
>Multiply both sides by inverse A
>Assume not, bottom row has all 0, which can multiply by no matrix to get In, contradiction on invertibility
>explicit construction on c)
>Multiply by A inverse
>Multiply by A inverse
>Use d) and det(AB) =det(A)det(B)
>Otherwise, we could use elementary tow ops to make a column of all 0s, then det=0
>Same as above but with rows
>Using h) and the fact we have n vectors, it follows immediately from some lemma I forgot the name of
>Same as above using i)
>H),j), definition of basis
>I),k), definition of basis
>h), definition of rank
>n) with rank nullity theorem, or simply use b) follows definition
>Basic arithmetic with orthogonal complements
>Basic arithmetic with orthogonal complements
>Follows immediately from o)
>Follows immediately from n)
>Follows from invertibility
>Use g) and Det(A-IL) = 0
>U)->a): Ax= 0 is never true for nonzero x, so we have all our pivots, so A is invertible.

How did I do, /sci/?