/sci/ - Science & Math

>>9669823
profs aren't gods, they're just people

>>9669823
...Well OP...? What is the difference? I actually want to know because I still don't understand.

>>9669825
Well I dont know bc my professor didnt fuckin answer me

>>9669823
A matrix doesn’t have to contain vectors. It can't, but it doesn't have to

A tensor is a describes a vector in relation to a geometric space.

I get confused when tensors start representing real physical objects but the argument is the same

>>9669829
edit

>it can, but it doesn't have to


sorry, i'm tired

>>9669829
Okay I'm a brainlet, please explain it to me in terms of programming

A vector is this for instance, size 3

float[3]

Then what is a tensor?

>>9669823
so he's a mathematician then?

>>9669832

A tensor is just a generalized version of vectors and scalars. i.e. a vector is a subset of a tensor.

>>9669832
hahahahahahahahahahahahahahahahahahahahahahahahahahahahahahaahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahaha

>>9669838
to elaborate you can generate a space using vectors, and the tensor describes their relationship to each other.,

So if you change your basis set, the vectors change, but the tensor doesn't

Who cares, nerd. Not even award winning scientists want or need to know trivial hair splitting definitions.

>>9669832
a tensor is a vector in higher dimensions as
>>9669838
badly pointed out
[math] v^\mu = (1,2,3,4) [/math]
is a vector but a tensor can look like this
[math] T^{\mu \nu} = \begin{bmatrix}
1 & 2 & 3 & 4 \\
5 & 6 & 7 & 8 \\
9 & 10 & 11 & 12 \\
13 & 14 & 15 & 16
\end{bmatrix}
[/math]
both correspond to 4 dimensions and both transform very well across coordinate systems (with a simple differential transformation)

in your example it would just be like 2 arrays

>>9669852
What? That's just a matrix or a vector<4> of vector<4>

>>9669838
To add to this:
Rank 0 tensor is a scalar
Rank 1 is a vector
Rank 2 is an nxm matrix of vectors
Rank 3 is an nxmxk matrix.

In general, you can can think of a rank g tensor as a g dimensional matrix of vectors, though it's impossible to visualize the array past rank 3.

>>9669852
>badly pointed out
Sorry, i'm physical chemist and your nerd ass wasn't responding yet

I should be answering questions about molecules and shit

>>9669856
it's a visual representation of a rank 2 tensor which causes the confusion
what would be the matrix representation of [math] T^{\mu \nu \lambda} [/math]
which is a valid and common tensor

>>9669861
i mean you were right but saying something is a subset of the other doesn't at all help him understand what the difference between a tensor and a matrix is
>using your under qualification as an excuse on something you are under qualified to respond to in your opinion
>mfw

>>9669862
So tensors are where:
Rank 0) Scalar
Rank 1) Scalars except N of them so it's a vector
Rank 2) Vectors except N of them so it's a vector of vectors, or a matrix like what you showed
Rank 3) The thing above except N of them so it's a vector of vectors of vectors, or a vector of the matrix you showed

Is this right or no? Do they have to be the same in all dimensions, like can the first two rows of the matrix you posted be a tensor too?

>>9669868
yeah i guess it's just an array of numbers that can be represented in the way you said but it's kind of a confusing definition
no the first two rows can't be a tensor as it doesn't make sense as that's 4x2 and tensors can't be shaped like that
i just used 4 dimensions because that's what you use in general relativity

>>9669883
Okay so it always has to be an N-dimensional cube?

>>9669897
By that I mean an N-dimensional cube with a size value equalling the Rank 1 vector size

?

>>9669897
it's not really a cube because as soon as you get into odd rank tensors it's not square
you wouldn't describe a vector as a cube nor would you describe a rank 3 tensor
[math] T^{ abc } [/math]

>>9669825
>What is the difference?
A (n,m) tensor is a linear map from vector space N and its dual space M to a field.
A matrix is a (1,1) tensor

>>9669908
What I mean is every 3 dimension increases it becomes a cube right?

0) Scalar = cube
1) Vector = line
2) Matrix = plane
3) Vector of matrices = cube
4) Vector of vectors of matrices = line
5) Vector of vectors of vectors of matrices = plane
6) Vector of vectors of vectors of vectors of matrices = cube

Yes/no?

>>9669823
What is his field?

>>9669912
you could describe a rank 4 tensor as a matrix of matrices or a cube of cubes using your definition before
i.e.
[math] T^{ \mu \nu \lambda} = (T^{\mu \nu 1}, T^{\mu \nu 2}, T^{\mu \nu 3}, T^{\mu \nu 4}) [/math]
where each [math] T^{ \mu \nu x} [/math] is a separate tensor
you can see this argument for a rank 4 tensor as i'm too lazy to write it out

>>9669912
...cube?
Think of it as
rank 1: vector
rank 2: rank 1 (vector) with its components being vectors
rank 3: rank 2 (matrix) with its compenents being vectors
etc

>>9669912
>>9669921
ah i see what you mean now. that's just a geometric simplification after rank 3 as you're just shrinking things down into a tensor and then going from there

>>9669908
Tensor is not linear, it's linear in each variable, therefore (p, q)-tensor is (p+q)-linear map.

>>9669923
What he means is that a rank 3 tensor in 3 space has 27 components. It would look like 3 3x3 vector matrices stacked on top of each other. Aka a cube.

>>9670580
can a tensor be represented as a logic tree, where each component branches off into another tensor and so on depending on the order?

>>9669919
primarily algebraic topology. also graph theory, geometric topology

>>9669823
>professor that will actually admit that he doesn't know something
Amazing desu

>>9669832
please don't make Computer Science look bad

>>9669823
>does excellent research, wins awards on papers
nice!

>>9669832
just fyi, nothing in the C standard library behaves like a vector with several components. E.g. "7 * float[3]" doesn't make sense.

>>9670969
?????????????????????????
is that uncommon?

>>9671728
Why would that make sense...? You can't perform arithmetic on types. You can safely do this though float[3][7]

>>9669823
You must be such a fag irl

>>9669832
scalar: double
vector: double[]
matrix: double[][]
tensor: double[][][][][][][]...[][][][][][][][][]

>>9671817
Nice CS-hate meme picture but I make more money than you and had multiple offers and I have a great work life balance, relaxed work environment, and get regular bonuses, raises, and promotions.

>>9671832
too bad that didn't cure your autism

>>9669864
But he was right tho

>>9671834
d-delet this

>>9671730
It's not uncommon at all.
Realize most /sci/posters are larping /pol/tards who have been programmed to hate "smug" "crooked" academia