# Recent content by Mumba

1. ### Linear Algebra - Polar decomposition

First i calculated the eigenvalues: I got (i-\lambda)(-i-\lambda)+1, so \lambda_{1,2}=+-\sqrt{2}i Is it correct to go on on like this: \lambda_{1}a+b=\sqrt{\lambda_{1}} \lambda_{2}a+b=\sqrt{\lambda_{2}} After calculating a and b, we plug it into f(x) = ax+b --> f(A^{*}A)=a(A^{*}A)+bI Then...
2. ### Linear Algebra 2 - Representing Matrix

oh man yes sure thx again ^^
3. ### Linear Algebra 2 - Representing Matrix

hmm, ok but why ist L(x) = x+1? --> p(x) = x if its a constant function and p(x)=x, shouldnt be P(x+1)=x too???
4. ### Linear Algebra 2 - Representing Matrix

Should it be like that: If p(x) =1 then, q(x) = p(x+1) = p(x)+p(1) = 1 + 1 = 2, so L= 2!?
5. ### Square root of a Matrix

Hey i just tried to calcuculate the eigenvectors. But i cant get a sol. The result is always = 0. ?? Edit: Forget it, using the way with a and b, i was able to solve it correct ^^ (without any eigenvectors)
6. ### Linear Algebra - Change of Bases

Cool :) Thx jbunniii
7. ### Linear Algebra - Representing Matrix

yeah its good thx mate!!! ;)
8. ### Linear Algebra 2 - Representing Matrix

:D:D cool thx alooooot
9. ### Linear Algebra 2 - Representing Matrix

ahh ok so if u change this fpr L(x^2) --> 1 2 1 matrix: 1 1 1 0 1 2 0 0 1 correct? ^^
10. ### Linear Algebra 2 - Representing Matrix

and then for L(1) --> 1 0 0 L(x) --> 1 1 0 L(x^2) --> 1 0 1 So my matrix would be 1 1 1 0 1 0 0 0 1 ??
11. ### Linear Algebra 2 - Representing Matrix

So i get then L(1) = 1 L(x) = x+1 L(x^2)=x^2+1 ?
12. ### Linear Algebra - Change of Bases

Coool thx a lot, easy this way. :D
13. ### Linear Algebra 2 - Representing Matrix

L(p)=q(p)=p(x+1)? wie kommst du da auf L(x)=1+x? Was hast du denn dann für L(1)?
14. ### Linear Algebra 2 - Representing Matrix

But so i get for L(x) = x^2 + x, L(x^2)=x^3 + x^2 So should i choose a new basis, for example {1+x,x^2,x^3} to get the repr matrix?
15. ### Linear Algebra - Change of Bases

the i get as matrix: 4/sqrt(2) 3/sqrt(2) 2/sqrt(2) 1/sqrt(2) correct?