Suppose $A$ and $B$ are invertible $n \times n$ matrices that are similar to each other. Then for example, $A - 2I$ and $B - 2I$ are similar, and $A^{-1}$ and $B^{-1}$ are similar. What other operations will preserve similarity, and what algebraic object is the set of all invertible similar matrices (i.e. is it an algebra over some field, etc.)
What preserves similarity of invertible matrices?
3
$\begingroup$
linear-algebra
-
1Their transposes should be similar, too... – 2011-10-14
-
2Let $f(x)$ be analytic, and defined $f(A)$ and $f(B)$ by their series expansions, then $f(A)$ and $f(B)$ are similar if $A$ and $B$ are... – 2011-10-14