Hello everybody,

i try to prove this statement:

if a Matrix M has a cholesky decomposition $\displaystyle M=L*L^t$, then the equation holds:

$\displaystyle (\| M\|_2) = (\| L\|_2)^2$.

Do you know, how i can prove this?

I Try this: $\displaystyle (\| M\|_2)^2 = \lambda_{max} (M^t * M)=\lambda _{max} (M^2)=(\lambda _{max} (M))^2

$

therefore $\displaystyle \|M \|_2 = \lambda_max (M)=\lambda_{max} (L*L^t)=\|L^t\|$.

but why is $\displaystyle \|L^t\| = \|L\|$??

is this correct? and why the last equation holds?

Regards.