Recent content by heshbon

Thanks greatly. That clears it all up.

I've had a thought about this, I guess what I am looking for is some sort of relation between the characteristic polinomial and the determinant of a the matrix.

is that complete nonsense?

Could i say the "size" of determinant express a measure of "how much" a matrix is invertable ?

Jordan Normal, Diagonal and Inverses Homework Statement 1) Is a diagonal matrix always invertable? 2) Is an Invertable matrix always Diagonalizable? 3) Is a matrix in jordan normal form always invertable The answers are prob straight foward but I am confused. Homework Equations...

1) Is a diagonal matrix always invertable? 2) Is an Invertable matrix always Diagonalizable? 3) Is a matrix in jordan normal form always invertable The answers are prob straight foward but I am confused.

Thats Great! Does the determinant imply anything about the linear map that induces it?

Homework Statement It's my understanding that 2X2 and 3X3 determinats kinda measure volume...is there a general interpretaion for an nxn determinant ( in words, not formulas please) Homework Equations The Attempt at a Solution

Well, the boundry point can't be real.., maybe i can say that the set is unbounded

Homework Statement Let I C R be an interval which is open and closed at the same time. Prove that I=R or I is the empty set. Homework Equations The Attempt at a Solution I'm looking more for a outline structure for the solution. I have made assumptions that I is not equal to R...

Is it possible to construct an algebraic system where zero is not unique, prehaps have a unique zero for every element which would than permit division by zero? Or maybe think of the zero as an operater rather than an identity element where the inverse would represent division by zero...

Division by zero is undefined...but why doesn't somebody just define it? Like they did with root (-1).

Homework Statement Suppose V=<Z> where Z is an infinite set, So Z spans V. Suppose that every pair of distinct elements of Z is linearly independent. Is it possible that V is finite dimensional? Justify your answer. Homework Equations The Attempt at a Solution All the vectors...

using sterlings equationm plus nth root test i get a limit which tends to infinity, but i think you can only conclude something about convergance of the sseries if the limit is real...

ln(e^x)=x; not 1. final solution shoud be ln(2)