wedge product example

When bivectors are defined by


so, for two generic covectors

\theta=a\beta^1+b\beta^2+c\beta^3 and \phi=d\beta^1+e\beta^2+f\beta^3,

we have the bivector




Cf. this with the data \left(\begin{array}{c}a\\b\\c\end{array}\right) and \left(\begin{array}{c}d\\e\\f\end{array}\right) to construct the famous


So, nobody should be confused about the uses of the symbol \wedge dans le calcul vectoriel XD


Filed under algebra, cucei math, differential geometry, math analysis, mathematics, multilinear algebra, what is math, word algebra

2 responses to “wedge product example

  1. Ray

    I would like to mention that using the wedge product, with understanding, allows one to determine dependency. For instance moving b^2 /\ b^3 to the right is only valid if
    bf-ce is not zero. This of course applies in the linear type case where the b,f,c,e are not functions of b2,b3.
    This is important when b1,b2,b3 are defined implicitly; say
    F(b1,b2,b3)=G(b1,b2,b3) =0 then dF/\dG can be expressed as the wedge products of the differentials dF/db1 db^1 ….dG/db3 db^3 and determine which variable are dependent/independent.
    By realizing that the wedge products talk about something like area (independence) one then gets a truly geometric viewpoint on things that looked like mysterious matrix manipulations.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s