transpose, .'
Symbolic matrix transpose
Syntax
Description
A.'A.
transpose( is equivalent to
A)A.'.
Examples
Transpose of Real Matrix
Create a 2-by-3 matrix, the
elements of which represent real numbers.
syms x y real A = [x x x; y y y]
A = [ x, x, x] [ y, y, y]
Find the nonconjugate transpose of this matrix.
A.'
ans = [ x, y] [ x, y] [ x, y]
If all elements of a matrix represent real numbers, then its complex conjugate transform equals its nonconjugate transform.
isAlways(A' == A.')
ans =
3×2 logical array
1 1
1 1
1 1Transpose of Complex Matrix
Create a 2-by-2 matrix, the
elements of which represent complex numbers.
syms x y real A = [x + y*i x - y*i; y + x*i y - x*i]
A = [ x + y*1i, x - y*1i] [ y + x*1i, y - x*1i]
Find the nonconjugate transpose of this matrix. The nonconjugate transpose operator,
A.', performs a transpose without conjugation. That is, it does not
change the sign of the imaginary parts of the elements.
A.'
ans = [ x + y*1i, y + x*1i] [ x - y*1i, y - x*1i]
For a matrix of complex numbers with nonzero imaginary parts, the nonconjugate transform is not equal to the complex conjugate transform.
isAlways(A.' == A','Unknown','false')
ans =
2×2 logical array
0 0
0 0
