mumblerfish@lemmy.world
on 03 Sep 2024 20:35
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A tensor is something that transform as a tensor. Gtfo Christoffel symbols.
vzq@lemmy.blahaj.zone
on 04 Sep 2024 05:36
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Duck typing ftw
marcos@lemmy.world
on 03 Sep 2024 20:50
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How you describe a thing is different from what a thing is… A tensor is not a matrix.
And on mathematics, “what a thing is” is a completely useless concept… So, it makes no difference whatsoever.
affiliate@lemmy.world
on 04 Sep 2024 17:00
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the “categorical” way of defining tensor products is essentially “that thing that lets you turn multi-linear maps into linear maps”, and linear maps (of finite dimensional vector spaces) are basically matrices anyways. so i don’t see it as much of a stretch to say tensors are matrices.
(can you tell that i never took a physics class?)
muntedcrocodile@lemm.ee
on 04 Sep 2024 00:07
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Everything’s a matrix if u fuck with it hard enough
Everything’s a matrix if you realize there is no spoon
UnRelatedBurner@sh.itjust.works
on 04 Sep 2024 10:16
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Sadly, they patched the spoon exploit.
ZILtoid1991@lemmy.world
on 04 Sep 2024 11:31
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You can still use movd, movq, movups, etc.
tatterdemalion@programming.dev
on 04 Sep 2024 07:52
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Square matrices are linear endomorphisms. They are isomorphic to (1,1) tensors but not any other rank of tensors.
affiliate@lemmy.world
on 04 Sep 2024 16:46
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a tensor is a multi-linear map V × … × V × V^^ × … × V^^ → F, and a multi-linear map V × … × V × V^^ × … × V^^ → F is the same as a linear map V ⊗ … ⊗ V ⊗ V^^ ⊗ … ⊗ V^^ → F. and a linear map is ““the same thing as”” a matrix. so in this way, you can associate matrices to tensors. (but the matrices are formed in the tensor space V ⊗ … ⊗ V ⊗ V^^ ⊗ … ⊗ V^^, not in the vector space V.)
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The difference between a matrix and a 2d array of numbers is the operations that are performed
A tensor really isn’t standardized in the same way so it’s basically just an n-d array in my mind
It’s all just pointers with semantics attached.
Vectors with strides.
Well, it would still be a vector. So some standardisation.
You can force a 2D array to be a matrix if you’re clever enough
good ol’ nominal typing
A tensor is something that transform as a tensor. Gtfo Christoffel symbols.
Duck typing ftw
How you describe a thing is different from what a thing is… A tensor is not a matrix.
And on mathematics, “what a thing is” is a completely useless concept… So, it makes no difference whatsoever.
the “categorical” way of defining tensor products is essentially “that thing that lets you turn multi-linear maps into linear maps”, and linear maps (of finite dimensional vector spaces) are basically matrices anyways. so i don’t see it as much of a stretch to say tensors are matrices.
(can you tell that i never took a physics class?)
Everything’s a matrix if u fuck with it hard enough
Everything’s a matrix if you realize there is no spoon
Sadly, they patched the spoon exploit.
You can still use
movd,movq,movups, etc.Square matrices are linear endomorphisms. They are isomorphic to (1,1) tensors but not any other rank of tensors.
a tensor is a multi-linear map V × … × V × V^^ × … × V^^ → F, and a multi-linear map V × … × V × V^^ × … × V^^ → F is the same as a linear map V ⊗ … ⊗ V ⊗ V^^ ⊗ … ⊗ V^^ → F. and a linear map is ““the same thing as”” a matrix. so in this way, you can associate matrices to tensors. (but the matrices are formed in the tensor space V ⊗ … ⊗ V ⊗ V^^ ⊗ … ⊗ V^^, not in the vector space V.)