
1.7.21 Linear transformations
condition: Vector systems \( \left\{\overline{a_{1}}, \overline{a_{2}}, \ldots\right\},\left\{\overline{b_{1}}, \overline{b_{2}}, \ldots\right\} \) are specified by their coordinates in the standard basis \( \left\{\overline{e_{1}}, \overline{e_{2}}, \ldots\right\}\). Find the linear transformation matrices \( \phi \) in the bases \( \left\{\overline{e_{i}}\right\},\left\{\overlin e{b_{i}}\right\},\left\{\overline{c_{i}}\right\} \), if in the basis \( \left\{\overline{a_{i}}\right\} \) it has the form a) \( \left(\begin{array}{cc}-3 & -3 \\ -4 & 1\end{array}\right) \), and \( \overline{a_{1}}=(-1,0), \overlin
Linear transformations of matrices in the transition between bases, coordinates of vectors and linear operators.