Hi. Define a linear mapping F: M2-->M2 by F(X)=AX-XA for a matrix A, and find a basis for the nullspace and the vectorspace(not sure if this is the term in english). Then I want to show that dim N(F)=dim V(F)=2 for all A, A≠λI, for some real λ. F(A)=F(E)=0, so A and E belongs to the nullspace. Then I define a basis for M2, as the 2x2-matrices B=(B11, B12, B21, B22) which has a 1 at i,j and 0's elsewhere. Well, this is how Im supposed to do, but it confuses me.(adsbygoogle = window.adsbygoogle || []).push({});

How should I view the basis-matrix? For example with linear independency. Lets say we define A to be the 2x2-matrix with elements (a,b,c,d) and map them with F. We get 4 matrices F(Bij) and I want to sort out which ones are linearly independent, with the condition A≠λI. How do I show L.I for matrices?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Using matrices as basis

**Physics Forums | Science Articles, Homework Help, Discussion**