ctranspose, '
Symbolic matrix complex conjugate transpose
Syntax
Description
A'A.
ctranspose( is equivalent to
A)A'.
Examples
Conjugate 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 complex conjugate 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 to its nonconjugate transform.
isAlways(A' == A.')
ans =
3×2 logical array
1 1
1 1
1 1Conjugate Transpose 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 conjugate transpose of this matrix. The complex conjugate transpose operator,
A', performs a transpose and negates the sign of the imaginary portion
of the complex elements in A.
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 complex conjugate transform is not equal to the nonconjugate transform.
isAlways(A' == A.','Unknown','false')
ans =
2×2 logical array
0 0
0 0
