vector product defined on kronecker delta

Asked Jun 09 '15 at 19:19

Active Jun 09 '15 at 21:47

Viewed 71 times

I have some vectors such as :

a={{0}, {0}, {0}};
b={{1}, {1}, {1}};
c={{1}, {1}, {0}};

I wanted to product a by a with the result 1, also the product of b and b must be 1, but the product of c and b (c and a) must yield 0, and so on. As a matter of fact, the desire result is as Kronecker delta, but I do not know how I can define a function with this characterization.

However, Jens' answer how-to-define-an-orthogonal-basis-in-the-right-way could help, but it is different in details, because, in my calculation any vector does not have a specified name same as x, y, z. In my large calculation, any vector acts with their component in any iteration and they do not have a name in every time. For example in how-to-define-an-orthogonal-basis-in-the-right-way output you can write:

tensorExpand[Dot[x, y]]
0

tensorExpand[Dot[x, x]]
1

But directly:

tensorExpand[Dot[{{1}, {1}, {1}}, {{0}, {0}, {0}}]]

can't manipulate.

edited Apr 13 '17 at 12:55

Community

asked Jun 09 '15 at 19:19

Unbelievable

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Question is very unclear. What do components of your "vector" mean? Are you inventing scalar product? Why Dot is no good? – BlacKow Jun 09 '15 at 19:25
Because, dot ('.') ,sums all product component after multiplication, but I didn't sum of them – Unbelievable Jun 09 '15 at 19:33
@BlacKow, please note 'I THINK, question is very unclear', because someone maybe understands completely without any ambiguous deduction. – Unbelievable Jun 09 '15 at 19:35
What about SameQ? – BlacKow Jun 09 '15 at 19:36
1

Maybe something like delta[v1_, v2_] := Times @@ MapThread[Boole[Equal[##]] &, {v1, v2}]. I am not sure I understand the question. – chuy Jun 09 '15 at 19:43
1

Or even delta[v1_, v2_] := Boole[Equal[v1, v2]]... – chuy Jun 09 '15 at 19:46
SameQ could help but is not straightforward, – Unbelievable Jun 09 '15 at 19:47
1

Boole@SameQ[#1,#2]& – BlacKow Jun 09 '15 at 19:48
@ chuy, this comment completely satisfy my needs. – Unbelievable Jun 09 '15 at 19:49
Maybe the following will be better suited for your ultimate goal (this is just a guess): How to define an orthogonal basis in the right way? – Jens Jun 09 '15 at 20:15
@Jens, I could not use of what you answer on the 'How to define an orthogonal basis in the right way'? However, that answer is so complete but many of them are not directly related to my question. – Unbelievable Jun 09 '15 at 21:01

vector product defined on kronecker delta

0 Answers0