# 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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### Properties of DFT of Circularly Symmetric 2-D Matrices

I'm very new in image processing and trying to get a grasp in the basic concepts in 2-D DFT. As far as I understood, DFT of a circulant matrix should also be a circulant matrix. But when I define a ...
269 views

### Smallest Eigenvalue in the Derivation of the MUSIC Algorithm

I am seeking clarification on a particular step in the derivation of the MUSIC algorithm as presented in a specific paper. Here, there is an intermediate step I cannot follow and I would appreciate ...
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### Harris corner detection shape of $E(u,v)$

I am taking a computer vision class and I have just learnt about the Harris corner detection concept. A corner is detected when a small shift in a window function defined around the corner results in ...
51 views

### Transform a data set by exploting the vectorfield

I am somewhat new in the field of Digital Signal Processing / Image processing. As shown in the figure, I have 4 straight lines $f_i(x)$ with $i = 1,\dots, 4$ that pass through $g(x)$. Similiarly ...
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### Image Matrix Vector Representation for the Degradation Model

I am trying to understand the the degradation model equation but I have doubt that how come y^t.x.h will be equal to x^t.h^t.y . Aren't they transpose of each other.
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### Minimize the Cost Function of Values of Vectors Based on Their Amplitude

I have two vectors $X = [x_1,x_2,x_3,x_4]$; and $Y = [y_1,y_2,y_3,y_4]$; I know that $|x_1|$ = $|y_1|$, and $|x_2|$ = $|y_2|$,... so on. it means the difference is only in the sign. it might be ...
1 vote
126 views

### A hypercomplex encoding to preserve spatial/temporal information? [closed]

I have recently come across the idea of encoding a 1D signal (i.e. a mono audio) as a complex vector instead of as a vector of reals, where the imaginary part is used to encode the cells' positions. ...
35 views

### What do coeffcients mean from Matlab?

I ask for a brief explanation of each coefficient and their sources of related information. Thank you very much in advance. The coefficients comes from this code below: I've got a robust linear ...
82 views

### On the simplification using trigonometric functions

Assume I have a matrix $D$ whose its entries are as below : Where $A$ and $B$ can be written using using the trigonometric functions for (1) as: My question, Is it possible to simplify (1) more? ...
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,...