1.4.28 Matrix Transformations

Condition: to prove that the formula \ (\ quad \ varphi (x) = a^{t} x a \) determines the linear transformation of the space of symmetric matrices \ (\ left (x^} = x \ right) \). Find Zordanov Bazis and Zordanov form of transformation. \ [A = \ Left (\ Begin {Array} {CC} 3 & 4 \\ -1 &1 \ END {Array} \ RIGHT) \]