Re: Analyse This!


me wrote:
Igor wrote:
me wrote:
Igor wrote:
me wrote:
Igor wrote:
standard deviation wrote:
Dirk Van de moortel wrote:

So his biggest blunder could well have been calling his
introduction of the constant his biggest blunder ;-)

Dirk Vdm

who tald yo that it shod be constatn?

that biggest blunder wol be that he called
it constant, which is not

Well, an additional term involving an arbitrary scalar function times
the metric tensor can be added to the Einstein equations and and still

you mean a factor, not a term,
you times factors not terms,
you add terms

No, I mean a term. Read it again.

i just did, yo are okay, i do appologise


what is scalar function, one taking
a scalar as input or returning a
scalar as output?

Yes.

which one of them is yes? both?

Yes to both.


how do you times a scalar
function on a tensor, please explain

Same as scalar multiplication on a vectot. It's an outer product. All
rhe components of the tensor get multiplied.

isnt that ilegal?

No. Sounds like you learn to learn some things about tensors.


a scalar times another scalar?

No.

scalars has no direction, nor dimension

Close, but I think that you might misunderstand what a scalar actually
is. It's an invariant number.

ok,but
a scalar is a rank 0 tensor
a vector is a rank 1 tensor
a matrice is a rank2 tensor
a cubic matrice is a rank 3 tensor, aka 3 dimensions etc

its ilegal ta multiply tensors with difrent ranks, thay
dont have the same domain of definition

Again, it's not. You can form a new tensor by multiplying two tensors
of different ranks. This is called an outer product. You end up with a
new tensor with rank equal to the sum of the ranks of the two tensors.

you make things more clear for me, but still

even tensors of same rank cant be multiplyed,
unless same domain defined

please explain

tensor A: rank 2, 2x2
tensor B: rank 2, 3x3

you cant multiply them like that, you pad A with zeros?

Have you ever heard of a tensor product, sometimes referred to as a
direct product? You'll find more info here:

http://en.wikipedia.org/wiki/Tensor_product

.

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