# 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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### 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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### 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 ...
384 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 $X_1$, $X_2$, $X_3$ ...
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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) ...
239 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 ...
432 views

### 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/...
206 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 ...
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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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### 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 ...
748 views

### 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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### 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 ...
306 views

### 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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### 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 ...
102 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?
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### Maximising each element in a matlab array

Is it possible to construct an array A, without looping, where A(i,j) = max(B(i),C(j)) and B ...
770 views

### How to compute regions of matrix

Let's say we have the following matrix: 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 I want to calculate the ...
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### Calculating covariance matrix for MVDR beamforming

I am trying to calculate the covariance matrix that is required for the calculation of an MVDR beamformer. I am getting confused as to how to calculate it. I have an array of 3 microphones each with a ...
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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 ...
194 views

### How can I get the uncertainties for peaks on an image?

When pick the peak points on an image, e.g. the matrix made by peak in matlab as this one, I can use max to get the index of ...
143 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.
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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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### 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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### 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 ...
158 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 ...
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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 ...