- #1
christang_1023
- 27
- 3
- Homework Statement
- A square matrix ##A## is said to be
• an involutory matrix if ##A^2 = I##,
• an idempotent if ##A^2 = A##.
Show that every involutory matrix can be expressed as a difference of two idempotents.
- Relevant Equations
- The involutory matrix can be decomposed to ##A=\frac{1}{2}(I+A)-\frac{1}{2}(I-A)##
I feel confused about proving the two terms are idempotents.