What is the significance of the basis vector e_{11} in a bivector?

[Jhenrique]

What is the basis of a bivector?

For example (see the attachment and http://en.wikipedia.org/wiki/Bivector#Axial_vectors first):
$$e_{11}=\begin{bmatrix} 1 & 0 & 0\\ 0 & 0 & 0\\ 0 & 0 & 0\\ \end{bmatrix}$$
or
$$e_{11}=\begin{bmatrix} 1\\ 0\\ 0\\ \end{bmatrix}$$
or $e_{11}$ is equal to what?

Thanks!

 

[tiny-tim]

Hi Jhenrique!

What is the basis of a bivector?

The basis is $\mathbf{e}_i\wedge \mathbf{e}_j$, for all i ≠ j

(wikipedia writes that as $e_{ij}$, which i find confusing )

For example, the electromagnetic 4-vector (E;B) is:​

$E_x\mathbf{i}\wedge\mathbf{t}+E_y\mathbf{j}\wedge\mathbf{t}+ E_z\mathbf{k}\wedge\mathbf{t} +$ $B_x\mathbf{j}\wedge\mathbf{k}+ B_y\mathbf{k}\wedge\mathbf{i}+ B_z\mathbf{i}\wedge\mathbf{j}$

 

[Jhenrique]

I asked what is e11 in terms of matrix...

 

[tiny-tim]

e₁₁ doesn't exist

e₁ $\wedge$ e₁ = 0​