telling if two matrices are congruent and computing the N matric s.t A=N$^T$BN

36 Views Asked by At

i guess that to matrices are congruent if and only if they have the same signature, but then if i know that they are congruent, how can i find the N matrix?

for example having $A = \begin{bmatrix} 10 & 7 \\ 7 & 5\end{bmatrix} $ And $B=\begin{bmatrix} 1 & 5 \\ 0 & 1 \end{bmatrix}$ how can i find N?( i just can do a system of equations or there's another way?)