1.11.11 Tensor calculus
Problem:
Given the tensors:
\[
\left(C^{i j}\right)=C=\left(\begin{array}{cc}
3 & 0 \\
-1 & 5
\end{array}\right), \quad d_{i j}=D=\left(\begin{array}{cc}
5 & -6 \\
3 & 1
\end{array}\right) .
\]
Calculate convolutions \( a_{k}^{j}=C^{i j} d_{i k}, \quad b_{k}^{i}=C^{i j} d_{k j} \), and scalar \( u=C^{i j} d_{i j} \).