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.
153
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Analytical expression for the eigenvectors of a 3x3 real, symmetric matrix?
I am writing an algorithm that process 3D images based on the local moment of inertia.
I have a 3x3 real symmetric matrix, from which I need to find the eigenvalues. I have found a variety of ...
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Why do we deal with the eigenvectors of the autocorrelation instead of the data itself?
How intuitively to understand why eigenvectors of the autocorrelation matrix are used, but eigenvectors of the matrix constructed from temporal samples have no sense and aren't used? For example, in ...
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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 $X_1$, $X_2$, $X_3$ ...
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7
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1
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Relationship between discrete deconvolution and Toeplitz matrices
I have 2 vectors, $a$ & $c$, both of length $M$. I know they are related by $a*b=c$. My goal is to recover $b$. Obviously $b = \mbox{deconv} (c,a)$. I am only interested in the first $M$ elements ...
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What is a covariance matrix?
Suppose you have k samples from each of the N elements of a uniform linear array (ULA) of sensors:
What is the physical meaning of a covariance matrix?
How do you form a covariance matrix with the ...
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2
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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.
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7
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1
answer
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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 ...
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1
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2D Convolution as a Doubly Block Circulant Matrix Operating on a Vector
I was reading Fundamental Image Processing, Chapter 5 (Image Transforms), I encountered the following problem:
Given the arrays $x_1(m,n)$ and $x_2(m,n)$ as follows:
Write their convolution $x_3(m,n)...
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6
votes
2
answers
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Circular Convolution Matrix of $ {H}^{H} {H} $
We all know that Discrete Fourier Transform (DFT) corresponds to circular (not linear) convolution. That is to say, if $x(n),h(n)$ and $y(n)$ is the original signal, the filter and output signal in ...
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Shortest geometric distance from surface in 3d dataset?
I have a three-dimensional binary image of a collection of discrete, individual voxels ("seeds") contained in a connected 3-dimensional surface ("skin").
(Like a small fruit, with a surface delineated ...
- 43
4
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2
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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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1
answer
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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 $l_1$-...
- 189
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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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2
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Why do we need to estimate eigenvalues?
I am not working in signal processing field, but recently I happen to read a paper which estimates source numbers using Gerschgorin radii, and I feel kind of confused about why we need to estimate ...
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1
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understanding FFT2 function of Matlab
I am trying to understand what happen when we take FFT2 of a matrix in a matlab.
first have a look at this simple example,
a=ones(8); %8x8 Matrix of Ones
fft2(a)
...
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votes
1
answer
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Is it possible to detect the sparse vector based on a non-invertible matrix
Given a non-invertible matrix $X \in \mathbb{R}$, let's say that matrix is, e.g. :
$X = \begin{bmatrix}
0.7500& -0.2500 &-0.2500 & -0.2500 \\
-0.2500& 0.7500& -0.2500 & -0....
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3
votes
1
answer
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5.1 Rear To 5.1 Side mixing matrix
I am searching for a matrix definition for converting a audio signal (5.1 with rear) to a audio signal (5.1 with side).
Currently I am using the definitions from: https://msdn.microsoft.com/en-us/...
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3
votes
1
answer
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Wave Digital Filter Bridge-T Resonator implementation, gives expected cutoff frequency but incorrect gain and roll-off
Trying to implement the WDF in Fig 5(a) of this publication. The response of the ideal op-amp implementation is given by the black curve in Fig 7:
Here is the plot I get when trying to implement the ...
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votes
1
answer
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Estimating a Matrix from Scaled Permuted Matrix
The problem is the non- negative matrix factorization of a matrix. Let me explain my problem I have an original matrix $A=\begin{bmatrix}
0.248437 &0.25198098 & 0.25396825 & 0.25077881\\
0....
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3
votes
1
answer
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Matching 2 Undirected Weighted Graph in MATLAB
Consider 2 undirected weighted graph as shown in figure. Consider first graph as $G_1$ and second graph as $G_2$. Graph $G_1$ consist of vertices $V=\{F_1,F_2,F_3,F_4,F_5\}$ and graph $G_2$ consist of ...
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0
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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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A good reference for matrix completion [closed]
Does anyone know a complete reference or book on matrix completion?
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1
answer
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Is There a Way to Perform a 2D Image Rotation by Matrix Multiplication?
In my understanding, unlike shifting and scaling, image rotation actually rotates the coordinates whereby interpolating the pixels at discrete positions. It is like a projection that discrete values ...
- 133
3
votes
0
answers
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Distribution of a signal covariance matrix
A common estimation problem in signal processing assumes the following signal model
\begin{equation}
\mathbf{r} = \sum_{i=1}^{Q}\alpha_i\mathbf{s}\left(w_i\right)+\mathbf{n}
\end{equation}
where $\...
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votes
2
answers
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Why is this matrix invertible in the Kalman gain?
In the wikipedia article about Kalman filters, the well-known expression of the matrix of Kalman gains is given:
$$ \mathbf {K} _{k}=\mathbf {P} _{k\mid k-1}\mathbf {H} _{k}^{\text{T}}\mathbf {S} _{k}^...
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1
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why use svd() to invert a matrix?
In MATLAB, i compared elapsed time to invert a Hermitian matrix using inverse(), svd(), and chol(). svd() took the longest. So is there any reason to prefer svd() to the other two methods?
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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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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 ...
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votes
1
answer
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What does "kernel based" mean?
In my thesis I try to explain what kernel based methods are, especially the meaning for object detection.
I know kernel based methods like Mean- and CamShift and I know how to use them. I understand ...
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2
votes
1
answer
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Reflection Rotation matrix
I'm doing a rigid body between point clouds using SVD.
Sometimes the routine produces an incorrect rotation matrix with a Determinant=-1, ie a reflection matrix.
Any idea why ?
Is there a valid way ...
- 824
2
votes
1
answer
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Proving that the uncertainty can not increase during the update step of a Kalman filter - positive semidefiniteness
I am trying to prove mathematically that the update step in a Kalman filter can not result in a increase in uncertainty. I found the following proof which is based on the inversion lemma and the ...
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votes
1
answer
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linear convolution toeplitz matrix vs circular convolution toeplitz matrix
I have an issue in understanding the difference between building the Toeplitz matrix when the convolution is linear and when it's circular. As I know that Toeplitz matrix $H$ can be built as following
...
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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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1
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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 ...
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2
votes
1
answer
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Matrix form of STFT
IS there a Matrix form of the STFT that could be applied to a signal directly, as in the case of DFT? We know the matrix structure of the DFT Matrix. Can we derive that somehow for a STFT Transform? ...
- 153
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votes
1
answer
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Deconvolution using Toeplitz matrices [duplicate]
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 look like a gaussian).
I tried ...
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votes
1
answer
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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 ...
- 485
2
votes
1
answer
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Dominant eigenvectors of an unknown matrix
Do you have any idea about how we can find the principal eigenvectors of an unknown matrix ${H}$?
The elements of $H$ are unknown in general. If you are familiar with channel estimation procedure in ...
- 21
2
votes
1
answer
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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 ...
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What is an analysis dictionary or operator in compressive sensing?
I am doing research on compressive sensing. I am new in this field. I read several papers regarding analysis dictionaries.
Here are some papers that I have read so far:
https://www.hindawi.com/...
2
votes
0
answers
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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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0
answers
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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 ...
2
votes
0
answers
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Help Understanding Radial Gaussian Filter
I am currently reading through Mueller's "Fundamentals of Music Processing" and I am trying to understand audio segmentation through the use of self-similarity matrices.
Currently, my matrix looks ...
- 21
2
votes
0
answers
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Can Cholesky outer product version result in negative square roots?
Say A is symmetric positive definite matrix , which means one necessary condition is diagonal entries of A are positive. If I do cholesky factorisation using outer product form, Can there be any ...
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vote
2
answers
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Optimization of square matrix multiplied with another matrix to have the final result a unitary matrix
I have a square matrix $D$ whose size is $m \times m$ multiplied with another $m \times m$ square matrix $C$, I need to optimize the matrix $C$ to have a unitary matrix $DC$. I mean optimize the ...
- 598
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Covariance matrix explanation
I am trying to understand and visualize the concept of a covariance matrix. Suppose I have a matrix:
$A = \begin{pmatrix} 2 & 3 & 4\\ 5 & 5 & 6 \end{pmatrix}$
how do I calculate its ...
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3
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What is the complexity of big-$O$ $O(N \times \mathrm{log}_2(N))$ vs real operations
I usually see books/references writing the complexity of such operations as $O(N \times \mathrm{log}_2(N))$; For example, the complexity of FFT/IFFT operation is $O(N \times \mathrm{log}_2(N))$. ...
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2
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The inverse of an orthogonal matrix is its transpose
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 ...
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vote
3
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Why do convolution kernels such as Gaussian, Laplacian, LoG almost always seem to be expressed in integers?
I'm a total newb in search of some deeper understanding, but I'm not able to read the maths behind these on Wikipedia.
If I understand correctly, you get the new value for each pixel by multiplying ...
- 141
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vote
2
answers
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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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