1.11.12 Tensor calculus

Problem: Given the tensors: \[ C=\left(C_{i j}\right)=\left(\begin{array}{cc} 3 & 0 \\ -1 & 5 \end{array}\right), \quad A=\left(a^{i}\right)=(3 ; 1) . \] Calculate convolutions \( a_{j}=C_{i j} a^{i}, \quad b_{i}=C_{i j} \cdot a^{j} \), and scalar \( u=C_{i j} \cdot a^{i} \cdot a^{j} \).