# Basis of bivector

1. Jan 20, 2014

### 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!

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2. Jan 21, 2014

### tiny-tim

Hi Jhenrique!
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:​

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

3. Jan 21, 2014

### Jhenrique

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

4. Jan 21, 2014

### tiny-tim

e11 doesn't exist

e1 $\wedge$ e1 = 0​