Recent content by crazygrey

Hi all, If a square matrix A of dimension n*n is a nilpotent matrix,i.e, A^k=0 for k>=m iff A has eigenvalues 0 with multiplicity n and index m or less. I did prove by induction if A^k=0 then all the eigenvalues are zero. I'm lost when I want to prove the oppesite, i.e, if all eigenvalues are...

Any help ?

Hi folks, I have to find the generalized solution for the following Ax=y : [1 2 3 4;0 -1 -2 2;0 0 0 1]x=[3;2;1] The rank of A is 3 so there is one nullity so the generalized solution is: X= x+alpha.n (where alpha is a constant , and n represents the nullity) I found the...

Really appreicate your help, that was very helpful . Thanks

1) I wanted to prove that all eigenvectors in the vector space are linearly independent, not a multiplication of it with a scalar. If I have a set of vectors [v1,v2,v3,--vn] 1,2,3,..,n are indices...this set of vectors belong to a vector space , and I want to prove that all of them are linearly...

1) Basically the idea is that having different eigenvlaues will results in independent eigenvectors. I just want to prove this thoerm. Let v=[v1 v2 v3...vn] set of eigenvectors with distinct eigenvalues w1,w2,w3,...,wn. By induction: if n=1, v1 has to be linearly independent since it is a non...

Hi everyone, I had couple questions: 1) If I want to proof that egienvectors are linearly indpendent by induction, how do so? I do understand that I can start with a dimension of 1 and assume v1 to be a non zero vector so hence a linear indepedent, what do I do after that for other cases...