Question

Here's a matrix problem: "Suppose A is idempotent. Let C=1/√2 * <|> (note: each <> identify a column in the matrix). Show that C is an involution.

Answer 1

If C is an involution C*C=I ¿right?

Answer 2

yep !

Answer 3

but what does
<<I,A>|<A,-I>>
mean? because my guess isi if you square it and use the fact that
\[A^2=A\] it should pop right out

Answer 4

Then, why don't follow this? C*C=1/√2 * <<I,A>| * 1/√2 * <<I,A>| =I, given that A is Idempotent, A*A=A

Answer 5

The equallity should be fulfilled after perform all matrix operations

Answer 6

@satellite73 <<I,A>|<A,-I>> means