i am new to this forum and not exactly sure if this post belongs here. i need a concrete idea for a determinant. i understand the determinant as the volume of the parallelopiped in the n dimensions corresponding to the order of the determinant. but is there an alternate idea?

while working with polygonal numbers and determinants i found that the 3*3 order determinant of any 9 consecutive n-polygonal numbers is -(3*(n-2))^3.

i was trying to understand what this result could mean but since my idea of the determinant is vague i was trying to go backwards and understand the determinant. anyway does this result have anysignificance? i proved this by obtaining a general form for an n- polygonal number and then estimating its determinant.

Show me how you derived your original definition of a determinant:

I haven't seen that way of looking at them. Is that from Analytical Geometry?

Show me how you derived your original definition of a determinant:

Unless I'm completely misunderstanding phaedrus, I don't see where s/he claims to have derived a new definition of a determinant.

 

More on determinants :http://mathworld.wolfram.com/Determinant.html

 

Phaedrus, I don't see any reason why your result should mean anything special. In general, the k-th n-gonal number is linear in n. So a 3X3 determinant of n-gonal numbers will be a cubic in n. What exactly do you find interesting ?

the determinant is the linear action of the inherited action of the map on the last component of the exterior algebra. does that help?