Jim Caprioli at The Finland Station

At the moment, I haven't got a clue about the essence or meaning of the Exterior Power and Symmetric Power. I have searched for explanations in Mathworld, PlanetMath and Wikipedia but without success. There is an Appendix about the subject in the book but not very useful for newbies. - I have Faith ( ...) that there will come a day, a moment of a-ha!, a sudden understanding of the concept. I had a rather strong a-ha! with Group Actions, that was a real eyeopener for me. I hope to find answers, clues in the lecture notes from Maria Gorelik, and I have the book Multilinear Algebra from W. Greub with several chapters about the subject. ( These little setbacks seem to effect other areas of my life since whatever I do I'll be worrying about Exterior and Symmetric Powers. )