Ask Your Question

Revision history [back]

click to hide/show revision 1
initial version

I asked this very same question on Math Stack Exchange and someone else pointed out my very silly mistake: When constructing the matrix P_B I omitted a minus sign for the last entry of the second row. The correct matrix is P_B = Matrix([[5/9, -4/9*I, -2/9*I],[4/9*I, 5/9, -2/9],[2/9*I, -2/9, 8/9]]), which is both idempotent and self-adjoint, i.e. represents and orthogonal projection with respect to the standard basis of $\mathbb{C}^3$.

I asked this very same question on Math Stack Exchange and someone else pointed out my very silly mistake: When constructing the matrix P_B I omitted a minus sign for the last entry of the second row. The correct matrix is P_B = Matrix([[5/9, -4/9*I, -2/9*I],[4/9*I, 5/9, -2/9],[2/9*I, -2/9, 8/9]]), which is both idempotent and self-adjoint, i.e. represents and an orthogonal projection with respect to the standard basis of $\mathbb{C}^3$.