Problem: (1) Since the matrix is semidefinite , it can be diagonalized with positive transformation :
(2) Since the matrix is positive semidefinite , it can be diagonalized with a unitary transformation :

Do (1) and (2) mean the same thing?
A: no

Problem: (1) In 1882 he was named the Quebec Superior Court for Joliette district , later in Montmagny , Kamouraska and Gaspe districts .
(2) In 1882 , he was named to the Quebec Superior Court for Joliette district , later serving in Montmagny , Kamouraska and Gaspe districts .

Do (1) and (2) mean the same thing?
A: yes

Problem: (1) The expressed Fourier can be further approximated as
(2) The Fourier expressed can be approximated as :

Do (1) and (2) mean the same thing?
A: yes

Problem: (1) Trencianske Jastrabie is a village and municipality in Trencin District in the Trencin Region of northwestern Slovakia .
(2) Trencianske Jastrabie is a village and municipality in the district of Trencin in the region of Trencin in northwestern Slovakia .

Do (1) and (2) mean the same thing?
A:
yes