Recent content by Gramsci

Hurkyl: I'm grateful, but I can't say I understand your point of the message. I feel really stupid for not understanding this.

Some notation in there that I'm quite not used to. What's really confusing me are some concrete examples, say, how to use (any given) definitions to form the tensor product of say, C^2 and C^3.

Landau: Thanks, I'll read it through. I'd love to see some "concrete" examples too if possible.

Hello, I'm currently reading Halmos's book "Finite dimensional vector spaces" and I find it excellent. However, I'm having some problems with his definition of the tensor product of two vector spaces, and I hope you could help me clear it out. Here's what he writes: "Definition: The tensor...

And oh, there's a small follow up-question: "What does this result say in general about the solutions of linear equations?" I'd say that if we have n unknowns and m equations, there's a non-trivial solution, but that's just me.

Then we have to know that it has a non-trivial solution, right? Is there any way to know that besides reasoning that builds on "matrices"?

Tedjn: Linear systems! Then if each y_j(e_i) produces a constant real number, we have a system of linear equations in n unknowns with m equations, right?

Tedjn: I've used the properties to rewrite them into the form: a_1y_1(e_1)+...+a_ny_1(e_n) = 0 etc. for all functionals. But still, nothing. Office_Shredder: I don't really understand what you're hinting at, sorry.

I've reached that point before, but from there I'm kinda stuck. My first thought was letting the first m entries of the vector be 0, but that wouldn't do anything. I thought something about representing each linear functional as a linear combination of the dual base vectors, but well, not...

Homework Statement Prove that if m < n and if y_1,...,y_m are linear functionals on an n-dimensional vector space V, then there exists a non-zero vector x in V such that [x,y_j] = 0 for j = 1,..., m Homework Equations The Attempt at a Solution My thinking is somehow that we...

When I do as we said, I get the matrix: 3 -1 2 -5 2 -3 1 -1 0 1 0 1 But my matrix should be the transpose of that. Anyone willing to help?

yes,it does.

Ah, it transforms it. I don't see where this is leading me, however :/

I'm not sure I understand. What set?

Homework Statement The matrix A =(1,2,3;4 5 6) defines a linear transformation T: R^3-->R^2 . Find the transformation matrix for T with respect to the basis (1,0,1),(0,2,0),(-1,0,1) for R^3 and the basis (0,1),(1,0) for R^2. Homework Equations - The Attempt at a Solution I have no...