1. Brief description
Matrix transpose in Matlab symbolic operation
transpose a vector or matrix
B = A.'
B = transpose(A)
Explanation
B = A.' returns the nonconjugate transpose of A, that is, the row and column indices of each element are swapped. If A contains complex elements, A.' does not affect the sign of the imaginary part. For example, if A(3,2) is 1+2i and B = A.', then element B(2,3) is also 1+2i.
B = transpose(A) is another way of doing A.', which enables operator overloading for a class.
The complex conjugate transpose operator A' also negates the sign of the imaginary part of the complex elements in A.
The two commands have the same effect, pay attention to adding a "." to the first command. Usually, the real number matrix is usually transposed by A', which is the conjugate transposition. There is no difference in real number operations, but there is a difference in imaginary numbers.
For symbolic operations, when performing matrix or vector transposition, the conjugate transpose command will be "conj(a)" in the matrix after transposition, so symbolic operations cannot be continued.
2. Code
%% Learning objective: Transpose of matlab symbolic matrix
clear all;
A1=sym(magic(4))
B1=A1' % If it is a complex number, it is a conjugate transpose
C1=A1.' % The real transpose
A2=sym([6+6i,6;6-6i ,6])
B2=A2'
C2=A2.'
%% Learning objective: power operation of matlab symbolic square matrix
clear all;
a=sym('[x 4*x 4;4 4 x;4.0 x 4]')
y1=a^2
b=sym('[4 8;4 7]')
y2=2^b
3. Running results
