1.2 Special Property Matrices Orthogonal matrices:QE Rnxn is orthogonal if QQT-QTQ-I Semi-orthogonal matrices if QE Rmxn satisfies QQT=Ii or QTQ-In Unitary matrices:UE Cnxn is unitary if UUH-UHU=I Semi-unitary matrices if UE Cmxm satisfies UUH=Im or UHU=In Properties of unitary matrices: (1)U unitary台U1=UH (2)U∈Rmxm unitary÷U orthogonal (3)U unitary rows(columns)of U are orthonormal. 1 Special Matrices 6/601.2 Special Property Matrices Orthogonal matrices：Q ∈ R n×n is orthogonal if QQT = QTQ = I Semi-orthogonal matrices if Q ∈ R m×n satisfies QQT = Im or QTQ = In Unitary matrices：U ∈ C n×n is unitary if UUH = UHU = I Semi-unitary matrices if U ∈ C m×n satisfies UUH = Im or UHU = In Properties of unitary matrices: (1) U unitary ⇔ U−1 = UH (2) U ∈ R m×m unitary ⇔ U orthogonal (3) U unitary ⇔ rows (columns) of U are orthonormal. 1 Special Matrices 6 / 60