Homework Statement
a) Prove that if a polynomial f(lambda) has f(A)=0, then f(AT)=0
b) Prove that A and AT have the same minimal polynomial.
c) If A has a cyclic vector, prove that AT is similar to A.
2. The attempt at a solution
a) I know that I need to show that f(AT) =...
For the the equivalence part, I want to show that the difference of the Cauchy sequence and its subsequence is a null sequence. Let xn and xnk exist in the Cauchy sequence where xnk is also an element in the subsequence. Therefore, |xn - xnk| < epsilon for n, nk < N, so Cauchy sequence -...
Hi,
I need to prove that any infinite subsequence {xnk}of a Cauchy sequence {xn}is a Cauchy sequence equivalent to {xn}.
My problem is that it seemed way too easy, so I'm concerned that I missed something. Please see the attachment for my solution, and let me know what you think.
Thanks.
Hi,
I'm trying to prove that there's a bijection between the open interval (0,1) and the set of all sequences whose elements are 0 or 1 in order to show cardinality continuum.
So let C={a1, a2, a3,...|ai is either 0 or 1} which is the set of all sequences of 0's and 1's
and let...
I was reading that the "exchange rows" operation can be achieved through the other two operations: multiplication by a nonzero number and adding a multiple of one row to another.
Any thoughts on the actual algorithm for achieving an exchange of rows through these other two operations? I...