Recent content by jack_bauer

I'm wondering, is it possible a graph G and its complement G' to be complete?

To show that I think it might be sufficient to show that these two matrices (since they're similar) have the same characteristic polynomial. So... There's an invertible matrix P such that A= ((P^-1) B P) det(A-tI) det([P^-1 BP]-tI) det([P^-1 BP]-[P^-1tI P]) det([P^-1(B-tI)...

A matrix is diagonalizable when algebraic and geometric multiplicities are equal. My professor proved this in class today, but I did not fully understand his explanation and proof. Can someone please help?

A matrix is diagonalizable when algebraic and geometric multiplicities are equal. I know this is true, and my professor proved it, but I did not understand him fully. Can someone please explain?

yeah I'm sure. would I be able to use 1/a for O then?

Homework Statement Define V =R with vector addition a+b=ab and scalar multiplication za=a^z. Show that V is a vector space. Homework Equations a+b=ab, za=a^z The Attempt at a Solution I was able to check all the axioms but one, the additive inverse axiom where for all v in...

lol, yeah I know what you are talking about. I'm just really lost with this stuff right now. thanks man.

Homework Statement Find an example of subspaces W1 and W2 in R^3 with dimensions m and n, where m>n>0, such that dim(intersection of W1 and W2)= n Homework Equations dim(W1+W2)= dim(W1) + dim(W2)-dim(intersection of W1 and W2) The Attempt at a Solution Well what I know...