# 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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### 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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### How can I explain the result of of multiplications by matrices

I have a vector $x$ with size $N \times 1$, it's multiplied with a $Z$ matrix $N \times N$, the resulted $N \times 1$ vector is $y = Zx$. I know that each value of $y_i$, where $i = 0, 1, 2, .., N-1$ ...
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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: ...
1 vote
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### correlation matrix vs. correlation function?

Can someone help me understand the difference between a 1-dim autocorrelation function and a 2-dim autocorrelation matrix of a random process aka time series? My Leon-Garcia textbook defines CX(τ) and ...
1 vote
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### Calculate sampling lattice matrix in 2D

The pattern in which the sample points are distributed in 2 dims, is called a sampling lattice, and can be defined by a generator matrix.. In 2 dimensions, the generator matrix consists of 2 vectors. ...
1 vote
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### The rank of Fundamental Matrix

This question is regarding two view geometry where a point lying in the image plane of the first frame/ position of the camera is mapped onto the image plane of the second frame/ position of the ...
1 vote
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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 ...
1 vote
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### 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 ...
1 vote
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### Emulate signal loss of a pixellated detector in Python?

I have a matrix 64x64 where each cell represents the pixel of a pixellated detector. The spacial response of this detector decreases by going further from its center (that is, coordinates "31,31" or "...
1 vote
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### Sensor Data Fusion with Orientation Sensors in 3D Euclidian Space

Preconditions For measuring the position of a mobile device in 3D space, I utilize two sensors with different characteristics that measure device orientation. Sensor A (a combined sensor of ...
1 vote
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### Matrix expansion into bases

I have an image (that is a matrix), let's say of dimensions NxN. I then want to expand this matrix into M basis matrices (for the moment I'm still unsure how many M of these basis matrices I should ...
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### How to understand energy function in thin plate splines?

guys! I have carried out some experiments using matlab warp tools from here. But the results are not good, so I decide to read its original paper Principal Warps: Thin-Plate Splines and the ...
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### What is the possible application of eigenvalues?

I am a PhD in mathematics. Recently, we made an attempt to compute the eigenvalues of non-normalized discrete sine and cosine transforms. Surprisingly, the issue regarding three particular types, DCT-...
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### Python - Discrete deconvolution using Toeplitz matrix

Lets say I have 2 vectors (1D signals that are sigmoids): $s$ and $m$, both related through the relation: $m = s * r$, my goal here is to recover the vector $r$ (should be a gaussian $\rightarrow$ ...
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### model of a quasi static block fading channel in MIMO system

can I know what is the model of a quasi static block fading channel in a MIMO system, in function of angle of departure and arrival?
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### Converting 2 variables (obtained by ICA decomposition) named A_ffdiag and W_ffdiag into mixing/unmixing matrix

I have two variables as a result of an ICA (Independent Component analysis) decomposition (decomposed using joint diagonalization algorithm which uses frobenius norm formulation) named A_ffdiag and ...
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### Signal Processing on non-Euclidean domains

I have a very simple yet fundamental question. Suppose I have a vector of data $x \in \mathbb{R}^N$. Without additional information, I guess the majority of people think this vector as defined over ...
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### Estimating Correlation Matrices

I am trying to obtain the correlation matrices of two random signals. Both of them, $X$ and $Y$, are white Gaussian Noise, with unitary variance. However, they are correlated, with correlation ...
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### Matrix multiplication computational complexity based on radix 2

I am wondering, can we use Radix 2 based computational-complexity calculation for any matrix multiplication whose size is $N$ x $N$ ?? where $N$ = $2^K$ and $K > 1$ is an integer ?? Or it can only ...
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### Stability of $x(n) = A x(n-1)+b$

I am looking at the following system: $x(n) = A x(n-1) + b$ where x and b are vectors and A is a matrix. How can I derive the stability and causality conditions for such a system using Z transform? If ...
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### unitary matrix complexity multiplication

Having a unitary matrix $X$ whose size is $n \times n$ and a vector $z$ whose length is $n$, and let's have: $$y = X^H {\rm diag}(z)X$$ where $X^H$ is the conjugate transpose of $X$. My question,...
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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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### How to calculate the scale, rotation angle and translation between 2 images if we know the homography result matrix?result

I got the result of findHomorgraphy in OpenCv. As below: Homography transform matrix: [-1.1534205416542787 0.7834287271121142 527.9064589440736 -0.2415444621693116 0.16412191792642924 ...
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### Generating Wavelet family matrixes

We have unnormalized Haar matrix which, is for example, H4=[1 1 1 1;1 1 -1 -1;1 -1 0 0;0 0 1 -1] After normalizing it, we use for haar transform. I know how to ...
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### Are there condition numbers associated with the STFT, DWT?

Recently I learned that the DFT has good numerical stability since it can be represented as an orthogonal matrix, which has a condition number of 1. Is it possible to represent the STFT and DWT as ...
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### How to Prevent overflow/saturation in fixed point implementation of Fast Data Projection Algorithm

I am trying to implement an algorithm in real-time on a Fixed point DSP (The Blackfin from Analog Devices). The algorithm does a lot of stuff, but in the middle it performs an algorithm called "Fast ...