Could you give me a hand with finding the LU decomposition of the following matrix : enter image description here
where B belongs to R nxn and prove that det(A)>0.
I tried in following way:
tried to use the cholesky block decomposition:
L1*L1T = I => L1=L1T=I
L1*L2T=L2T=BT => B = L2
L2*L1T=-B => L2 *I = -B=> -B=L2 (I got stuck here )
To make sure the indication will be correctly read i drawn it in Paint, sorry for that, but I don't know how do it in other way. enter image description here
What is wrong with my thinking?