# Questions tagged [linear-algebra]

is a branch of algebra, concerning linear nature of objects: vector or vector spaces, linear transformations, systems of linear equations, quadratic and bi-linear forms, among the main tools used in linear algebra is the determinants of the matrix pair. The theory of invariants and tensor calculus is usually considered as integral parts of linear algebra.

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### Decomposing Sobel Filter

I am trying to decompose a Sobel filter into two vectors (column and a row) using Matlab. If our Sobel filter is A = [1 0 -1; 2 0 -2; 1 0 -1] we can get the U, S, V ...
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### Converting Hadamard Product into Matrix Multiplication in Image Deconvolution with Total Variation (TV) Using ADMM

I would like to solve the following Image Deconvolution equation by ADMM. $$\mathbf { \min\frac{1}{2}\Vert{Cx-b}\Vert_2^2+\Vert w\circ (D x)\Vert_1 \tag 1}$$ Where, $x$ is a vector of unknown pixel ...
458 views

### Generate the Matrix Form of 1D Convolution Kernel

As a follow up to Generate the Matrix Form of 2D Convolution Kernel, could someone explain how to generate the matrix form of a 1D convolution kernel? How different convolutions shapes are handled? ...
33 views

### 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 ...
107 views

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### Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm - Fix Given Code [closed]

This is my implementation which doesn't work: ...
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### Sequential Form of the Least Squares Estimator for Linear Least Squares Model

I'm currently working on a project in which I need to find the tilt of a surface. Let's assume I'm only concerned with a single dimension tilt (i.e. slope) to begin. I currently have the ability to ...
214 views

### How to implement discrete extended kalman filter in matlab

I have a nonlinear system, and I need to use the extended kalman filter to estimate it. I know I need the jacobian, but once I get that, is everything else the same as the normal kalman filter? I ...
133 views

### Check whether a given equation is linear

$a = (x, y) \in \mathbb{Z}^2$ is given as a pixel. My equation in which $g$ is image(matrix) is defined as, $f(x, y) = 56g(x,y)+93g(x−1,y)+92g(x+1, y)−57g(x, y−1)+555g(x, y+1)$ How can we know ...
91 views

### DFT as an Orthogonal Basis Change

In one of the homeworks that I am dealing with for Linear Systems course, I have encountered with such a statement: Consider $\mathbb{C}^N$ the vector space of N dimensional complex vectors. We can ...
209 views

### Conversion from stationarity to non-stationarity

Is there any way to convert a non-stationary signal to a stationary one, perform operations on it meant for a stationary signal and then convert it back to the non-stationary one?
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### How to Check Separability of 2D Filter / Signal / Matrix

Given: x(n1,n2) = {1 ,n1=0,n2=0 ; 2 ,n1=1,n2=0 ; 3 ,n1=0,n2=1 ; 6 ,n1=1,n2=1 } How could one prove it is ...
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### How do I apply a binary mask and STFT to produce an audio file?

So here's the idea: you can generate a spectrogram from an audio file using shorttime Fourier transform (stft). Then some people have generated something called a "binary mask" to generate different ...