In linear algebra, a matrix $B$ is said to be "similar" to $A$ if $B=C^{-1}AC$, that is $B$ = a matrix $A$ multiplied by a third matrix $C$, and its inverse, $C^{-1}$.
In regular algebra, if I take a number $x$, and multiply it by $\frac{1}{2}$ and then $2$, the latter terms cancel out, and I get $x$, the same and not a "similar" variable. Wouldn't you also have this result in linear algebra? What am I missing?
Best Answer
Matrix multiplication is not commutative in general. It corresponds to function composition, which is clearly not commutative in general.