In this thesis, we discuss Kadison’s Carpenter’s Theorems and their relation to majorisation in infinite dimensional Hilbert spaces. As it is well-known the Pythagorean Theorem states that; If a and b are the lengths of two sides of a right angle in the right triangle and c is the length of the hypotenuse of the triangle, then a 2 + b 2 = c 2 then we offer a new proof of his striking characterisation of the set of diagonals of orthogonal projections on Hilbert space.
