# Questions tagged [matrix]

is a mathematical object to be recorded in a [usually] rectangular array of elements of ring or field, which (table) is a set of rows and columns are located at the intersection of its elements. The number of rows and columns specify the size of the matrix.

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### What is the order of the output of HoughCircles in OpenCV, when having several circles on a frame?

So I am trying to use stereo vision to calculate the depth of several red balls. With the function HoughCircles, I get an output at one frame from one of the cameras like for example: ...
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### 2D FFT Toeplitz Matrix Indexing

I have a convolution sum_j M(x_i-x_j) v(x_j) which I would like to numerically compute using a FFT. x_i and ...
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### Derivation of Toeplitz Matrix

I'm having a difficult time understanding why the matrix for LTI systems is a Toeplitz matrix. I can see why $h_{n,m} = h_{n' + q,m' + q}$ given that $n' = n - q$ and $m' = m - q$, and \sum_{m'= -\...
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### Clarifying matrix notation from an ICA-CMN paper

In the paper I am referring (and here from citeseer), complex vectors $\mathbf{z}$ and matrix $\mathbf{M}$ were defined as follows \begin{align} {{\bf z}} &= \left[z_{1},z_{2},\ldots,z_{N}\right]^...
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### How to reduce time consuming for calculating pseudo inverse of large matrix in matlab?

I have a matrix P = randn(45875x65536 ); Pi = pinv (P); I tried to run this code in matlab, but it takes long time is it possible to split the matrix into ...
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### Correlation of a signal

I have one sample for a signal. This sample is a vector of length 384. I need to calculate the correlation matrix for this signal,So I need many samples for the same signal. How can i generate these ...
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### Image processing - Why is sum of values of a blurring filter = 1?

Usually, blurring filters have the sum of all the values in the filter matrix equal to $1$. Why is it so?
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### How Is Mixed Norm (${L}_{1, 2 }$) Better than ${L}_{1}$ Norm for Sparse Representation?

Using ${l}_{1}$-norm regularization for the purpose of achieving sparsity of the solution has been successfully applied a lot. But many times, I found the paper using mixed-norm instead of $l_1$-...
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### What is about the circular convolution in OFDM

In an OFDM system, serial-to-parallel conversion for data is done, then the DFT is performed and then adding the cyclic prefix (CP). My question is related to that step of adding a CP. As I know, ...
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### how to set Equalizer's coefficient using generalized eigenvector.

In that paper https://jwcn-eurasipjournals.springeropen.com/articles/10.1186/1687-1499-2012-72 .. Equation 3, $J(w) = w^HBw/w^HCw$ .. $B$ and $C$ are matrices, $w$ the filter coefficients vector ...
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### In OFDM, does $N N^H$ equal $I$?

I'm still new in OFDM and reading about it, but I have a question. In OFDM system, when having $N$ data symbol assigned to sub-carriers, $N$ should be orthogonal with each others, which means $NN=0$....
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### Designing a fast linear operator with $\pm 1$ entries with low condition number and low Hamming distance between consecutive rows

I need to design a matrix for compressive imaging where each row represents an $N$-pixel filter in a focal plane through which light is masked, summed, and measured (think of Rice's single-pixel ...
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### What is the relation between kernel functions, kernels used in convolution and null spaces of a matrix?

I have recently started learning about machine learning and have come across kernels and null spaces. I understand that null space is the set of all vectors that satisfy the equation A.v = 0 (Where A ...
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### Ifft through Matrix multiplication

I am still new to MATLAB, so apologies if I sound lazy to you. I am attempting to model a transformation as a set of matrix operations. I start with a vector, up-sample it by $U$ (up-sampling rate), ...
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### 1D as a 3D FFT - what’s wrong here?

I implemented the algorithm to calculate 2D DFT derived from 1D DFT. It works great, and makes my calculations much more efficiency then regular 1D DFT. But now I want to make 3D DFT derived from 1D ...
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### 1D as a 2D FFT - am I understand it properly

in one of my question about non $2^L$ points FFT I got answer with advice to read about that in following book: Rabiner, Lawrence R., and Bernard Gold. "Theory and application of digital signal ...
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### FFT - mixed radix - bit reversal

I wonder what is bit reversal for mixed radix FFT. Is there any algorithm that compute the bit reversal for various mixed radix FFT? Here should be mention why I want that. For example if I have ...
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### 3D world homography matrix calculation

I have a matrix in (x,y,z) coordinates and also i have a transformed version like (x_new,y_new,z_new). I need to calculate a transformation matrix that can transform (x,y,z) to (x_new,y_new,z_new). ...
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### AWGN channel matrix

For my current project work, I need to create an AWGN channel in MATLAB. There is a built-in function in MATLAB named 'awgn'. But that returns the value of received signal after passing through awgn ...
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### Join 2 NMF models where dictionaries has hierarchical structure

I have two NMF models $A = W_1A_{dict}$ and $B = W_2B_{dict}$ (where the $W$ represents weight coefficient matrix). What is a good way to join two NMFs if I know each column of $B_{dict}$ is summed up ...
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### Normalized LMS with a posteriori Error and Woodburry's Matrix Inversion

I was going through this paper and the author mentioned that we can prove the following using the Matrix Inversion Lemma (AKA Woodburry's Matrix Inversion Identity): Using matrix inversion lemma we ...
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### How to calculate the Diagonal loading factor evaluate calculate the inversion of a covariance matrix

I am programming a Generalised Likelihood Ratio Test (GLRT) detector. When it comes to inverting a covariance matrix $Ri$, I need to do a diagonal loading to fix the problem of sigularity of this ...