Symbolic matrix complex conjugate transpose
Conjugate Transpose of Real 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.
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 1
Conjugate Transpose of Complex 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
A', performs a transpose and
negates the sign of the imaginary portion of the complex elements
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
A — Input
number | symbolic number | symbolic scalar variable | symbolic matrix variable | symbolic expression | symbolic vector | symbolic matrix | symbolic multidimensional array
Input, specified as a number or a symbolic number, scalar variable, matrix variable (since R2021a), expression, vector, matrix, multidimensional array.
Complex Conjugate Transpose
The complex conjugate transpose of a matrix interchanges the row and column index for each element, reflecting the elements across the main diagonal. The operation also negates the imaginary part of any complex numbers.
For example, if
B = A' and
then the element