(i,j) element of DFT Matrix

[Sauraj]

Hello, what is the values of (i,j)'th element of the DFT Matrix?

 

[Deleted member 4993]

Hello, what is the values of (i,j)'th element of the DFT Matrix?

Please explain - What is a DFT matrix!

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment

 

[Sauraj]

DFT Matrix is:

Here transformation matrix example is for 4 points on the unit circle.
I think value of (i,j) inthe matrix is i^(i*j) where first i is the complex number.

 

[HallsofIvy]

Clearly it is NOT "\(\displaystyle i^{ij}\)" because if it were the first row (and column) would be \(\displaystyle i^{1*1}= i\), \(\displaystyle i^{2*1}= -1\), \(\displaystyle i^{3*1}= -i\), and \(\displaystyle i^{4*1}= 1\)!

 

[Steven G]

You have the DFT matrix in your post #3. At this point isn't it obvious what the ij entry of the matrix is? For example the (3,2) entry is -1.

 

[Sauraj]

No, I know that if the Matrix is for \(\displaystyle \Omega_{n}\) then the entries can be calculated with \(\displaystyle ω_{n}^k=e^{-2{\pi}i*k/n}\) but is it possible to find out the entry of some \(\displaystyle \Omega_{n}\) matrix with some fomula if only indices (i,j) are given? sorry for my stupidity.