# 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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While watching through the computer vision lecture on interest point detection, computing $E(u,v)$ requires computing the quantity $$E(u,v) = \sum_{x,y}(I(x+u,y+v) - I(x,y))^2$$ In the lecture, $I(x+u,... 1answer 19 views ### Harris corner detection shape of$E(u,v)$I am taking a computer vision class and I have just learnt about the Harris corner detection concept. A corner is detected when a small shift in a window function defined around the corner results in ... 1answer 38 views ### Transform a data set by exploting the vectorfield I am somewhat new in the field of Digital Signal Processing / Image processing. As shown in the figure, I have 4 straight lines$f_i(x)$with$i = 1,\dots, 4$that pass through$g(x)$. Similiarly ... 2answers 21 views ### Image Matrix Vector Representation for the Degradation Model I am trying to understand the the degradation model equation but I have doubt that how come y^t.x.h will be equal to x^t.h^t.y . Aren't they transpose of each other. 1answer 48 views ### Minimize the Cost Function of Values of Vectors Based on Their Amplitude I have two vectors$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|$,... so on. it means the difference is only in the sign. it might be ... 0answers 73 views ### A hypercomplex encoding to preserve spatial/temporal information? [closed] I have recently come across the idea of encoding a 1D signal (i.e. a mono audio) as a complex vector instead of as a vector of reals, where the imaginary part is used to encode the cells' positions. ... 1answer 26 views ### What do coeffcients mean from Matlab? I ask for a brief explanation of each coefficient and their sources of related information. Thank you very much in advance. The coefficients comes from this code below: I've got a robust linear ... 4answers 63 views ### On the simplification using trigonometric functions Assume I have a matrix$D$whose its entries are as below : Where$A$and$B$can be written using using the trigonometric functions for (1) as: My question, Is it possible to simplify (1) more? ... 0answers 60 views ### unitary matrix complexity multiplication Having a unitary matrix$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,... 1answer 41 views ### Calculate the Derivative of Gradient Field of an Image I meet a confusing thing in image processing recently.... Assume the image$x \in \mathbb{R}^n$, with its derivative (difference) matrix:$D^+ = \begin{bmatrix} D_h \\ Dv \end{bmatrix} \in \mathbb{R}...
if $\mathbf x$ is $N\times 1$ sparse vector, and $\mathbf A$ is an $M\times N$ matrix with $M<<N$, and we measure $\mathbf y=\mathbf{Ax}$, then compressed sensing theory tells us that we can ...