# Euclidean Norm or Norm 2 of Matrix

I have this matrix:

$T = \left( \begin{smallmatrix} -1&-3\\ -3/5&-1 \end{smallmatrix} \right)$

I would like to find the Euclidean Norm (Norm 2) of T. I know the expresion $\sqrt{λ(AA^{t})}$

$TT^{t} = \left( \begin{smallmatrix} -10&18/5\\ 18/5&34/25 \end{smallmatrix} \right)$

But I'm confused with the next steps, could you help me with that, if you could make some calculus I will be grateful a lot.

To proceed from here you simply find the eigenvalues of the matrix $TT^t$ and then take the square root of the largest eigenvalue. Since
$$||T||_2 = \sqrt{\lambda_{max}}$$
I wont't go into the computation of the eigenvalues but the largest eigenvalue of $TT^t$ is $11.30$ so the $2$-norm is
$$||T||_2 = \sqrt{11.30} = 3.36$$