5 votes
Accepted

The Matrix Form of a 2D Circular Convolution

Yes, indeed. You may represent the convolution in a Matrix Form. Pay attention that this form assumes the image is column / row stacked into a vector. If you're after a circular convolution, you may ...
  • 42.6k
3 votes
Accepted

What is the complexity of multiplication a real matrix with real vector

If you multiply an $M \times N$ matrix with an $N \times 1$ vector you get a vector of size $M \times 1$ For the generic case you will need $M \cdot N$ multiplications and $M \cdot (N-1)$ additions. ...
  • 34.1k
2 votes
Accepted

Expressing mathematically the number of real addition operation for a vector after dividing it

The number of additions is just the length of the individual vectors times their number minus $1$: $$\textrm{number of additions}=N\cdot\frac{2^l-1}{2^l}$$ Of course we assume that $N$ is a power of $...
  • 81k
2 votes

Deriving the Matrix Inversion Lemma for RLS Equations vs the Woodbury Derivation

I'm not sure if the OP was looking for a proof or derivation. In my mind a derivation is bit different than what Royi provided. I have looked for but never seen a derivation of the various versions of ...
  • 2,761
2 votes
Accepted

How can I express the flipped output of multiplication in function of original inputs?

You just need to conjugate the matrix $D$ as well as the vector $x$, and flip the rows of $D$ upside down, i.e., the first row becomes the last row, etc. I.e., you need to introduce a new matrix $\...
  • 81k
1 vote
Accepted

Can we recover a vector from one element of resulted vector after multiplication?

I think the answer is there is no way to recover $s$. Here I will be using a superscript $*$ to indicate the complex conjugate. First lets expand the matrix multiplication: $$y_1 = \frac{1}{2}\left[(...

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