GitHub - hanyoseob/python-transpose: Tranpose operator

Reference

1. Inner product

   • https://en.wikipedia.org/wiki/Inner_product_space

2. Transpose

   • http://en.wikipedia.org/wiki/Transpose

3. Complex conjugate

   • https://en.wikipedia.org/wiki/Complex_conjugate

1) Inner Product definition

    < X, Y >  = < [x1; x2; ...; xn], [y1; y2; ...; yn] >,  

              = [x1; x2; ...; xn]' * [y1; y2; ...; yn],  

              = SUM_(i=1)^(n) xi * yi,   

              = (x1 * y1) + (x2 * y2) + ... + (xn * yn).

2) Transpose definition

If A satisfies the following relation,

    < A * X, Y > = < X, AT * Y >,  

then,

3) Complex conjugate definition

Transpose for Matrix ver.

If A is defined as follow,

then,

Transpose for Function ver.

1) differential function

If A(x) is defined as follow,

then AT(y) is that,

2) Fourier transform

If A(x) is Fourier transform,

then AT(y) is Inverse Fourier transform,

3) Radon transform

If A(x) is Radon transform called by 'Projection',

    A(x) = radon(x, THETA)
    
    where, THETA is degrees vector.

then AT(y) is Inverse Radon transform without Filtration called by 'Backprojection',

    AT(y) = iradon(y, THETA, 'none', N).
    
    where, 'none' is filtration option and N is image size.