Understanding Transformation Matrix Order for B and B'

[liltyke115]

I was just wondering that when we take P, the transformation matrix from B to B', does B and B' have to be ordered from the highest thing?

What I mean is that I have B = 1, 1+x, 3+4x+2x^2 When I do the actual transformation, must I order it and do 2x^2+4x+3 first?

 

[StatusX]

What are you talking about?

 

[HallsofIvy]

The highest "thing"? Is that some technical math term I don't know? I THINK you are talking about a vector space of polynomials with given polynomials as basis vectors. There is no requirement that the polynomials be in order of increasing or decreasing degree. In fact, for most vector spaces, there is no "natural" way of ordering vectors. The matrix form of a linear transformation WILL depend one the basis: both on the specific vectors and the order. So be sure that you specify how you are ordering the basis vectors.