Easy way to multiplying standard basis

It seems to be easy, but I am not good at it.

I would like to generate the following matrix that is multiplying of two standard basis:

    E_{ij}:= (e_i - e_j)(e_i - e_j)^T

Could any body knows how to write it in few lines?

Thanks

[Azzi Abdelmalek]

What is T?

[Saber]

It shows exactly the transpose of the first term or in MATLAB like a'.

[Azzi Abdelmalek]

What is the size of e. Can you provide an example?

[Saber]

@Azzi Abdelmalek: Please look at below

[Azzi Abdelmalek]

Post an example with expected result

[Azzi Abdelmalek]

It seems that second Wayne's answer is what you are looking for

Answer 1

[Thiru jeyan]

You can use this method

e=@(k,n) [zeros(k-1,1);1;zeros(n-k,1)]

For an example

>> e(1,3)

ans =

     1
     0
     0

>> e(2,5)

ans =

     0
     1
     0
     0
     0

Answer 2

[Wayne King]

I agree with the comment above that you should provide an example because it's not clear what the size of your problem is or how scalable you want it. For example, are you looking for something as simple as:

 E1 = [1 0 0]';
 E2 = [0 1 0]';
 matrx = (E1-E2)*(E1-E2)';

[Saber]

Let's our dimension is n=5. Now in this dimension we have five standard basis which all together build identity matrix I up. e_i shows this unit vectors(columns of I) that in i'th position is 1 and other entries are all zero. for example

e_3= 0
     0
     1
     0
     0

now I want to build up a routine way to create this vectors and label them as the position of 1's.

I hope that now it is clear a bit.

Answer 3

[Wayne King]

You can just do

I = eye(5);

Each column of I is a standard basis vector

Then,

idx = [3 4];
Is = I(:,idx(1))-I(:,idx(2));
X = Is*Is';

gives you what you want for an example where i=3 and j= 4

[Saber]

The out put is too strange:

X =

     0     0     0     0     0
     0     0     0     0     0
     0     0     1    -1     0
     0     0    -1     1     0
     0     0     0     0     0

I need to separate matrix

I =

     1     0     0     0     0
     0     1     0     0     0
     0     0     1     0     0
     0     0     0     1     0
     0     0     0     0     1

as unit indexed vectors

       1       0       0       0       0
       0       1       0       0       0
  e_1= 0  e_2= 0  e_3= 1  e_4= 0  e_5= 0
       0       0       0       1       0
       0       0       0       0       1

[Wayne King]

so just extract the columns, what is so difficult about that?

Did you look at the Is vector? that is just a column vector.