Definition
Two matrices are similar if there exists some matrix such that,
for some such that .
Similar matrices have the same trace, determinant, and characteristic polynomial. In particular, we can define , , or by using any of these matrices.
Two matrices A,B are similar if there exists some matrix S such that,
A=S−1BSfor some S,S−1 such that S⋅S−1=S−1⋅S=In.
Similar matrices have the same trace, determinant, and characteristic polynomial. In particular, we can define trT, detT, or fT(x) by using any of these matrices.