Lecture07
... sets of parentheses into a product of n+1 factors. For instance Cat(2)=2 since there are only two ways to put parentheses around three factors: ((ab)c) and (a(bc)). The book gives a formula for Cat(n), gives a recursive definition, and then gives a proof by induction that they two are equal. It is a ...
... sets of parentheses into a product of n+1 factors. For instance Cat(2)=2 since there are only two ways to put parentheses around three factors: ((ab)c) and (a(bc)). The book gives a formula for Cat(n), gives a recursive definition, and then gives a proof by induction that they two are equal. It is a ...
Pauli matrices
... where ~σ = (σx , σy , σz ) = (σ1 , σ2 , σ3 ). For proof, check L.H.S.=R.H.S.. Theorem: Any arbitrary 2 × 2 complex matrix can be written as the linear combination of four matrices I, σx , σy and σz . Therefore, it can be proved that (I, σx , σy , σz ) form an orthogonal basis for the complex Hilbert ...
... where ~σ = (σx , σy , σz ) = (σ1 , σ2 , σ3 ). For proof, check L.H.S.=R.H.S.. Theorem: Any arbitrary 2 × 2 complex matrix can be written as the linear combination of four matrices I, σx , σy and σz . Therefore, it can be proved that (I, σx , σy , σz ) form an orthogonal basis for the complex Hilbert ...
