## Test of rotation matrix multiplication
## Error in matrix multiplication
## There is some error with column-uncorrelated matrix multiplication.
version
## Complex rotation matrix
## Generate a complex rotation matrix
theta = randn * pi;
cs = cos (theta)
phase = sign (randn + i * randn);
sn = sin (theta) * phase
M = [cs, sn; -sn', cs]
##
## Check
abs (cs) ^ 2 + abs (sn) ^ 2 == 1
##
## Matrix products: M'*M, M*M'
M' * M
M * M'
##
## Element-wise products
Mt = M';
M (1, :) * Mt
M (2, :) * Mt
Mt * M (:, 1)
Mt * M (:, 2)
[Mt(1, :) * M(:, 1), Mt(1, :) * M(:, 2); Mt(2, :) * M(:, 1), Mt(2, :) * M(:, 2)]
## Real rotaion matrix
## Generate a real rotation matrix
theta = randn * pi;
cs = cos (theta)
phase = 1;
sn = sin (theta) * phase
M = [cs, sn; -sn', cs]
##
## Check
abs (cs) ^ 2 + abs (sn) ^ 2 == 1
##
## Matrix products: M'*M, M*M'
M' * M
M * M'
##
## Element-wise products
Mt = M';
M (1, :) * Mt
M (2, :) * Mt
Mt * M (:, 1)
Mt * M (:, 2)
[Mt(1, :) * M(:, 1), Mt(1, :) * M(:, 2); Mt(2, :) * M(:, 1), Mt(2, :) * M(:, 2)]
## Note
## M' seems to have unwanted numerical error in octave!
## The element-wise product is good, but matrix product has some error
## where the entries should be zeros.
## If we try real rotation matrix, it shows same.