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/sci/ - Science & Math

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File: 160 KB, 694x1036, 01-Numbers-1-Intro.jpg [View same] [iqdb] [saucenao] [google]
1104843 No.1104843 [Reply] [Original]

I've started writing a tutorial on how to do tensors, multilinear algebra, and differential geometry with diagrams (rather than long lines of algebra symbols)

This is the beginning of it. I still have a long way to go, but what does /sci/ think so far?

>> No.1104863
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>> No.1104847
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>> No.1104876
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>> No.1104877

meh, just learn in the regular way. things will make more sense farther down the line

>> No.1104880
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>> No.1104890
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>>1104877
Sure, but this makes it easier to read a lot of things.
Rather than juggling indices, you move lines.

>> No.1104901

not shit

>> No.1104903
File: 167 KB, 744x993, 07-Covectors-1.jpg [View same] [iqdb] [saucenao] [google]
1104903

I don't have any good examples of full tensors yet though.. Those will come in the future pages.

>> No.1104906

wtf is this shit?

>> No.1104910
File: 63 KB, 691x557, 08-Covectors-2.jpg [View same] [iqdb] [saucenao] [google]
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>> No.1104923
File: 79 KB, 748x708, 09-Vector Example-1.jpg [View same] [iqdb] [saucenao] [google]
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>> No.1104933
File: 71 KB, 692x601, 10-Covector Example-1.jpg [View same] [iqdb] [saucenao] [google]
1104933

The last picture was an example of a vector. This is an example of a covector that could multiply that vector.

>> No.1104943
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>> No.1104953
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>> No.1104960

whoa this is terrible, how can you expect tensors to make sense in this notation? really, matrices do the job way better, especially with tensors when "juggling indices" actually gives insight into what you're really doing

>> No.1104951

why?
why?

>> No.1104964
File: 118 KB, 730x972, 13-Zero Covector.jpg [View same] [iqdb] [saucenao] [google]
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>> No.1104991
File: 99 KB, 675x836, 14-Zero Vector.jpg [View same] [iqdb] [saucenao] [google]
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And this is the last one. Next I'll be working on basis vectors & then tensor products.

>>1104960
I've seen tensors in this notation. They work very nicely. Much better than juggling indices.
This has some nice pictures of tensors: http://en.wikipedia.org/wiki/Penrose_graphical_notation

>> No.1105006

build that shit out of wood
give to 3 year old son
watch him become professional physicist at the age of 10
???
profit

>> No.1105011

>>1104991

But...roger penrose is a troll..?

>> No.1105023
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>>1105011

>> No.1105031

>>1104839

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>> No.1105033

This is an interresting way of transforming abstract math into something more easily understood. Sure it was bit hard at first to understand the concepts but it may actually make the rules easier to understand and remember in the long run.

>> No.1105108

If I make more, I'll probably post the whole thing again in a few days to a week.

>> No.1105112
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>> No.1105122
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Post moar and archive now! This is gold, you fools!!!

>> No.1105137

>>1104960
Fuck you. I have god-tier spatial int, but juggling indices always confused the shit out of me. This way, tensors actually make sense.

tl;dr: Tensor in hell, math-fag.

>> No.1106238

The order in which you multiply things usually will matter, especially if you're talking about multilinear algebras.

>> No.1106341

I appreciate the effort, but I seriously doubt it could be of any use whatsoever in domains that need tensors.