Creating Matrix provided elements
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From a Hermititan (complex skew symmetric) matrix of order N (Asssume N=15) a column vector is created such that all the diagonal elements are placed first and then the ordered pair of real and imaginary parts of upper triangle matrix are placed next. Since it is hermitian matrix the upper and lower triangle elements have same set of real and imaginary elements.
For example for N=15x15 matrix the vector looks like this
[D1, D2, D3,...........,D15, R11, I11,R12, I12,.... ,R15, I15] in total 225 elements column vector.
How to construct back the matrix given this vector?
4 Comments
Jan
on 23 Jul 2021
What is R1_2 compared to L1_2? Should it be L2_1? If it is a hermitian matrix, why are the L elements stored?
Please explain exactly, what the inputs are. Use a 4x4 matrix to avoid the need to use unclear abbreviations.
Accepted Answer
Jan
on 24 Jul 2021
Edited: Jan
on 24 Jul 2021
A = rand(4) + 1i * rand(4);
A = A + A'; % Hermitian
% Convert to vector:
D = diag(A).';
L = triu(A, 1);
Lf = L(L ~= 0).';
Lv = [real(Lf); imag(Lf)];
VU = [D, Lv(:).'];
% And backwards:
n = sqrt(numel(VU));
L = triu(ones(n), 1);
L(L==1) = VU(n+1:2:n*n) + 1i * VU(n+2:2:n*n);
% Or: L(L==1) = [1, 1i] * reshape(VU(n+1:n*n), 2, [])
B = diag(VU(1:n)) + L + L';
isequal(A, B)
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