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 Matrix transpose AT = 15 33 52 −21 A = 135−2 532 1 Example Transpose operation can be viewed as flipping entries about the diagonal ie, (AT) ij = A ji ∀ i,j Definition The transpose of an m x n matrix A is the n x m matrix AT obtained by interchanging rows and columns of A, Definition A square matrix A is symmetric if AT = A Properties of transpose64 = S on a C B Squares on a Chess Board 24 40 = D and N of the G F Days and Nights of the Great Flood 25 76 = T in the B P Trombones in the Big Parade 26 50 = W to L Y L Ways to Leave Your Lover 27 99 = B of B on the W Bottles of Beer on2 29 if a ib=0 wherei= p −1, then a= b=0 30 if a ib= x iy,wherei= p −1, then a= xand b= y 31 The roots of the quadratic equationax2bxc=0;a6= 0 are −b p b2 −4ac 2a The solution set of the equation is (−b p 2a −b− p 2a where = discriminant = b2 −4ac 32 Predissociation An Overview Sciencedirect Topics 40'ã "¯Œ^ ƒc[ƒuƒƒbƒN —«