# 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.

96 questions
Filter by
Sorted by
Tagged with
13 views

### What is the difference between positive matrix coefficients and negative matrix coefficients of an audio?

I have turned an audio file into an one dimensional array by using audioread function in matlab and found several positive and negative fractional coefficient values.What is the basic difference of ...
353 views

### The Least Norm Solution of Under Determined Linear System

Suppose I have a matrix $$A= \begin{pmatrix} 1 & 0 & 1 & 0\\ 0 & 1 & 1& 0\\ \end{pmatrix}$$ where the variables are channel information like assume $X_1$, $X_2$, $X_3$ ...
18 views

### A good reference for matrix completion

Does anyone know a complete reference or book on matrix completion?
74 views

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

Can any one help me in deriving the matrix inversion lemma rule for RLS algorithm? I don't know how to start with. Many books have just stated but they haven't derived it.
61 views

102 views

### 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 ...
84 views

### 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?
138 views

### 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, ...
81 views

### 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 ...
78 views

### 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 $l_1$-...
43 views

### 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 ...
394 views

### 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), ...
46 views

### 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 $NN=0$....
67 views

### 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 ...
2k views

### Difference between correlation/convolution and matrix multiplication

Can anyone please clarify the difference between correlation/convolution and matrix multiplication? As I thought either convolution or correlation is similar to matrix multiplication. I read this ...
133 views

### 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 ...
157 views

### Digital Image Processing Framework

i'm looking for a free/opensource solution for digital image processing with reasonable performances processing quite large images (e.g. actual smartphones have resolutions of 8-10Mpx) and being ready ...
807 views

### Apply Low Pass (Smoothing) Filter on a Set of Matrices and Reject Outliers

Given a set of a $3$ by $3$ matrices ${H}_{i}$. Each matrix is an Homography matrix. They are used to stabilize Video Stream. Yet some of them are outliers which creates "Jumps" in the "...
197 views

### Least Angle Regression (LARS) without Matrix Inversion

Sorry if this is too damned long. I did what I could to abbreviate it. The question is about Least Angle Regression (LARS). I'm new to numerical work with matrices. I believe I have a way to ...
27 views

51 views

### 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 ...
67 views

### 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 ...
253 views

### 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 ...
848 views

### 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). ...
166 views

### Mechanics of a matrix Interleaver

I am having trouble understanding exactly how the matrix interleaver. I have read the following page from MathWorks. In it, it gives the following example where "123456" is interleaved as "142536." ...
197 views

### 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 ...
18 views

### 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 ...
49 views

### 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 ...
25 views

### Can I start testing my NMF with extension on sample that have only one source?

I am testing my supervised NMF algorithm to extract signal from observation that have only one source inside. I am new here and I wonder this is very weak model or not? Is it acceptable in signal ...
100 views

### How to make the $\ell_2$ norm of all columns and rows of an $n \times n$ matrix equal to $\sqrt{n}$?

I have an $n \times n$ matrix and I would like its columns and rows to have $\ell_2$ norm equal to $\sqrt{n}$. Is this possible?
161 views

### Deterministic method to compute “Process noise covariance matrix, Q” for a Kalman filter when parameter variations of the model is known apriori

I am implementing a Kalman filter (for a linear ODE system for now). My model represents a physical device that has 6 "parameters", i.e. those values of the device do not evolve over time (within a ...
152 views

### Relationship between matrix rank and beamforming

I always encounter the term matrix rank in papers related to beamforming. I am only familiar with the basics of beamforming (delay sum beamformer, basic capon). Can someone explain the significance of ...
957 views

### Accelerometer - coordinate system transformation

I'm getting some accelerometer readings from an Android phone, but it comes in on the phone's coordinate system. I want to apply a transformation to put the acceleration in the world coordinate system ...
573 views

### Noise estimation SNR matrix

I have a signal matrix which is a $256\times 192$, and I want to calculate the SNR considering that my $259\times 192$ matrix is an average of a $256\times 192\times 330$ matrix, where $330$ is the ...
62 views

### Linear Systems, Sparse Solutions, and $4 \times 4$ Sudoku Algorithm [closed]

I am unable to understand the paper Linear Systems, Sparse Solutions, and Sudoku. I have to form a $4 \times 4$ Sudoku using the algorithm in this paper. Can somebody please provide me the algorithm ...
179 views

### In 1D DCT, why is the input a vector?

The question is specific to this document: Image Compression. It is chapter 6 from book "A First Course in Applied Mathematics" by Jorge Rebaza. It is, a to the point explaination of DCT that is ...
150 views

### What is the best way to determine the process noise matrix $\mathbf Q$ of a Kalman filter?

It seems like most of the resources online suggest to determine the values of the process noise matrix $\mathbf Q$ through trial and error. However sometimes trial and error doesn't work, so I would ...
109 views

### How to prepare and plot unequally spaced, irregular data to a contour plot or similar with MATLAB

I've got a data set of hot-wire measurement velocity amplitudes at a given frequency bin (time data that has already been transformed to the frequency domain and I am just considering data for a given ...
931 views

### Sensing matrix for compressed sensing

What are the differences between random binary sensing matrix  and random Gaussian sensing matrix? What the advantages and disadvantages of each matrix? How can I choose the suitable matrix for a ...
In the following statement I don't understand the case for $\ i = j$: Let $\mathbf A$ be an $\ m \times \ n$ orthogonal matrix where $\ a_i$ is the $\ i^{th}$ column vector. The $\ ij^{th}$ element ...
$y(n)$ = output signal $x(n)$ = input signal $\mathbf H$ = system response as a toeplitz matrix \mathbf H = \begin{bmatrix}h(0)&&&\\h(1)&h(0)&&\\h(2)&h(1)&h(0)&\\...