 #1
Karl Karlsson
 104
 11
 Homework Statement:

If V = ##M_{n,n}(\mathbb R)## is the vectorspace of nxn matrices for some n and ##L(A) = A^T##, show that V is an internal direct sum
of the eigenspaces and show that L is diagonalizable.
 Relevant Equations:
 xxx
I was in an earlier problem tasked to do the same but when V = ##M_{2,2}(\mathbb R)##. Then i represented each matrix in V as a vector ##(a_{11}, a_{12}, a_{21}, a_{22})## and the operation ##L(A)## could be represented as ##L(A) = (a_{11}, a_{21}, a_{12}, a_{22})##. This method doesn't really work well when we talk about general ##n\times n## matrices. How would one go about to solve this?
Thanks in advance!
Thanks in advance!